Introduction to Vectors

[@renewd]

Unbelievable presentation!! I love the way you relate vectors immediately to trigonometry, using theta as direction. Other videos I have watched did not do this. I found it interesting that for the unit vector example you gave, a^2 + b^2 or (-3/5)^2 + ((-4/5)^2 = 1, Recalling the unit circle and Pythagorean. Thanks for reminding me about the 30-60-90 triangle. I know the relationships, but I forget to apply them. I did remember to use 45-45-90 triangle for the last example. You know how in church, the churchgoers say "Preach!". Your students say "Teach!"

[@profrobbob]

THANK YOU Chris for sharing your appreciation and your experience with us! Please take the time to like, subscribe and share this free resource with everyone, especially teachers...so ALL current and future students know how to find us...BAM!!! (I wish my students would shout out "teach"...simply paying attention and participating in class would be nice:)

[@mauricioalfonso8521]

I guess it's kind of off topic but do anybody know a good place to stream newly released movies online?

[@karsynbraydon8137]

@Mauricio Alfonso ehh try flixportal. Just google after it:P -karsyn

[@mauricioalfonso8521]

@Karsyn Braydon Thank you, I signed up and it seems to work =) I appreciate it!

[@karsynbraydon8137]

@Mauricio Alfonso you are welcome :D

[@dustyandrea]

I had a substitute for this lesson in my college trig course, along with a test the next class meeting. Profrobbob you have taught my class this lesson when the actual professor couldn't. You're the man!!!

[@profrobbob]

THANKS for studying and subbing!

[@profrobbob]

You're welcome! Building my channel has become like a second job, but hearing from students like yourself, makes all the extra work worth while:) Thank you for acknowledging and complementing.

[@rohmaxy9901]

Thanks a lot for the lesson on vectors. Really appreciate the time and effort you invested.

[@profrobbob]

You're welcome...please like, SUBSCRIBE and share to help my channel groW and help others:D

[@mathnerdwannabe2494]

I got it... I GOT IT! 30 years later and I’m finally understanding this stuff!!!! O...M...G!!! THANK YOU! 🙏🏾🙏🏾🙏🏾🙏🏾🙏🏾🙏🏾🙏🏾🙏🏾🙏🏾🙏🏾

[@profrobbob]

You are so welcome. I'd also call that a "BAM" moment:) I am thrilled you learned a lot from this lesson! I have made a lot of new good vector notes recently you may like. Check out the video description.

[@profrobbob]

You are very welcome. Thank you for watching and the kind words:)

[@GregorySerrano1986]

I can't even express how helpful this was. I was reading through my Larson textbook... made nearly no sense. Watched your video, and I'm golden. You are a real blessing.

[@profrobbob]

Gregory Serrano thanks for taking the time to seek out additional help and chose #ProfRobBob to like & learn from:) Please spread the word:D

[@profrobbob]

You're welcome...and I'm glad to see you are still watching and learning from my videos! (and I see you and my wife like alot of the same artists too:)

[@ielizabethm2]

I am watching your video of Introduction to Vectors before studying for my Calculus exam! This topic was done 5 months ago in class so of course, I have completely forgot some of them. Your explanations are clear and simple. Thank you sir, this was VERY helpful to me!

[@profrobbob]

You're welcome Elizabeth Medina and thanks for choosing #ProfRobBob to watch, refresh and study with! Now...Go pass that exam like BAM!!! ...and thanks for the clarification of "head to tail" (student teaching teacher, I do appreciate it:)

[@emeelzia]

I'm so mad I just discovered these videos! As an online precalculus student...this stuff is GOLD. The book can only teach me so much. Thanks for these! They're so helpful.

[@ello-isa]

Hi ProfRobBob, I wanna just say thank you for this amazing video, I started my engineering course 2 weeks ago, and this video helped me a lot to revise what my professor explained in class.

[@profrobbob]

Thanks for taking the time to "thank the teacher"...please take the time to sub and share this free study resource with your professor so all the students know where to find free after class help...even if it's just for a little while:) Good luck with that engineering degree too...keep up this kind of studying and you'll pass it like...BAM!!!

[@profrobbob]

Thank you. Some of my students think I'm long-winded too but they don't have the advantage of a fast-forward button!!! You say reverse...I say fast-forward...either way works...cause the long winded way just happens to be the way I teach. I look forward to your continued support and learning more from my videos. And no worries...NO MORE RED CHALK on my boards:)) Thanks.

[@profrobbob]

You're welcome:) I liked being referenced as "inspirational"! Thank you for "liking" and sharing my videos. I appreciate all the support from my viewers.

[@PhotonPhantom5]

Thank you SO much for making these videos. I have always loved math (it is what I love the most in school), but I do not learn well from my current teacher's style. I learned more here than I have the past three weeks at school, and I am going to refer my friends and the people I help out during class to your channel. Please keep these coming, and continue to brighten everyone's day with your personality!

[@profrobbob]

You are SO welcome PhotonPhantom5 and thanks for taking the time to watch my channel, send such a nice compliment and "thank the teacher"! If you really want to help this channel groW...as you are telling all your friends and class to watch please remind them to like, subscribe, support the ads, like on Facebook, share thru social media, tell their teachers and all of their friends and classmates...if EVERYONE keeps sharing we can keep GROWING and helping others just like you...BAM!!!

[@ILuvTheColorBlu]

Your videos are fantastic. You are the reason I am passing math.

[@profrobbob]

BAM!!! Thanks for watching and learning from Tarrou's Chalk Talk:)

[@darkomew8209]

You are one of the few KZbin math channels I actually enjoy. PS: I wish I had your handwriting. Thanks for the help!

[@meghansowersby]

Enjoyed every second of this entire video! Your channel helped me go from gettin a 68 to a 97! Thank you SO much. I've told everyone in my math class about you Mr. T!!

[@profrobbob]

Meghan Sowersby I'd say that calls for a giant BAM!!! and CONGRATULATIONS:)Thanks for the update and class support...proof once again that studying CAN make a difference, thanks for taking advantage of these additional resources and choosing my channel to help you, please keep sharing your success and my channel...students like you are why I love teaching:)

[@pomona2251]

I love the enthusiasm in your videos. It keeps the mood up and makes learning a bit easier.

[@matusz729]

THANKS!! I've never gotten a FULL explanation of all this stuff. Helps so much!!

[@McLovinDynamite007]

This is the best video explaining vectors that I've seen. Your videos are a huge help in my trig class.

[@profrobbob]

Thanks for studying and subbing to my channel! Please share this free study resource and your experience with your teacher so they can share it with ALL the rest of their current and future students too...we all benefit and grow...BAM!!!

[@TheIronicUsername]

I would have to agree 100% with you Flower ! I was considering dropping my trigonometry course because the professor would not explain the concept nor why we use them or why my father beats me when he comes home inebriated. On top of that the professor would constantly make weird noises that could only be described as "midlife echoes " that consisted of semi - audible whispers of him rambling on why he would never get tenure at the community college as he would do problems on the wooden board. But ever since i found ProfRobBob on here, I can quickly catch up to the course material and now have a deeper understanding when it comes to Trig and its applications like that one "man falling off a ferris wheel problem" where you calculate the time it would take for this man to meet his creator as he falls to the concrete ground. Thanks ProfRobBob !

[@profrobbob]

Flower and Trip...Thanks to you both and again, please share this free resource with all the math teachers you can:D

[@TheIronicUsername]

No problem boss! Me and Flower actually work as math tutors at our local community college and whenever our tutees take a break from complaining about how their professors are jacking off during lecture (meaning they aren't really teaching and are going off on tangential rants about their wives or soon to be ex - wives midway during lecture with absolutely no shame) we constantly recommend your KZbin channel for extra help to our tutees and they absolutely love you !

[@roinujzerimar2217]

Thank you this video really help I can't even begin to explain how helpful it was.

[@profrobbob]

..and THANK YOU for the complimentary review! You're welcome...glad to see you are still watching too:)

[@jasons2699]

The vector class with the best explanation I've ever learned! Thank you sir!!!!

[@Christian-en7vb]

ProfRob, you are definately top 3 best maths teacher on the internet. Your teaching skills are amazing. Thank you so much for your time and effort

[@profrobbob]

You are extremely welcome and thank you for subbing and taking the time to send a comment full of compliments and acknowledging our efforts!!! My wife and I have worked very hard for the last 6plus years trying to grow this channel and she answers all the general comments for me since I still teach full time. Please sub, share and keep spreading the word for us...BAM!!!

[@qnibly]

#1 on the internet, and real life from what Ive seen...

[@profrobbob]

No million subscriber award yet so I'm sure we haven't made it to #1...but we do work hard to keep growing and appreciate the help and positive reinforcement from grateful viewers like you...BAM!!!

[@qnibly]

Subscribers schmibers....a better measure of success is how many people are really helped by your videos. Also the fact that I got a 94% on both my math tests this week (Trig and Pre Calc) from watching your videos and practicing on Aleks. You are #1 because you really know how to teach, and your personality is very shiny. Also that you care to spend the time to help people all over the world by making these videos after hours from your classroom. And how thouroughly and consistently you cover the material, in an organized way. Man, you don't even know. You are teaching people who don't have access to this in their communities, or maybe aren't getting it the way their teachers explain. Def the best in my book! I wish I had your videos when I was homeschooled in the woods :D Hello to Cheryl, and thank your for your dedication and support to make it possible for us to get this help! Bless you both for your good work!

[@profrobbob]

You're the best!!! I was just showing Rob your latest comment and looked back to see how long you've been commenting and saw that I never replied to this one:( It was so awesome I even tried to pin it to the top of the page but because you replied to someone else's comment I couldn't...stupid YT...lol

[@profrobbob]

If you are given your vectors in component form like 2,3 you would move right 2 and up 3 just like you were plotting a point. A vector of magnitude 3 and a bearing of N20W would have a length of 3 and would be going to the up and a little left. It is like plotting a point but you don't have to start from the origin.

[@profrobbob]

If your angle is in quadrant 2, your reference angle is 180-theta...quadrant 3 ref angle is theta-180...quadrant 4 ref angle is 360-theta. If working with radians, which is likely, replace 180 with pi and 360 with 2pi.

[@IamChronos123]

You are the best!! I am going to start taking math classes online and teach myself with your videos!!

[@profrobbob]

THANKS I Am Chronos and thanks for choosing my channel to learn from and subscribe to...I also have a website that you might find easier to go directly to the subject. www.profrobbob.com Good luck with your class too!

[@peteristefanidis3549]

If It wasn't for you I would not be able to finish my class on time. Thank you so much for the hard work you put into these videos. I feel as tough I'm back in the class room.

[@user-we4cs5pj9l]

Thank you @profrobbob you're the reason why I'm doing good in vectors

[@profrobbob]

+Kimberly Geronimo thanks...but I can't take all the credit since YOU are the one that takes the time to study, nice job...BAM!!!

[@Nooreazy]

42 Minutes?!! I applaud you for being so dedicated.

[@BlooCowz]

Hey! Just wanted to tell you that EVERYONE appreciates how you reply and answer individual questions in the comments. We know it's not easy to do and I hope you get the M next to your name soon!

[@profrobbob]

THANK YOU Mikkloud~AMVs for noticing! Since we started we have made every effort to reply to all comments...this year it was hard to answer all the math questions but I appreciate the help other students offered too:D ...and please keep spreading the word till you see that M!!!

[@mn-yv2ur]

thank you professor Bob. you are such a great teacher 😊😊😊😊😊😊😊😊😊😊

[@profrobbob]

thanks for watching!

[@shelvidonmez1634]

I have binged a bunch of your videos and I cant help but feel so thankful for you and your teachings. I was seriously struggling with vectors but you taught this lesson so well I feel like a pro. Thank you so so much.

[@profrobbob]

Thank you for choosing my videos to learn from and your kind words. I hope you found all of my newer Vector videos I linked in the description. I relearned a lot about 2-D and 3-D vectors in the last 3 years because of a new class I am teaching. Thank you again!

[@profrobbob]

Yes...or PreCalculus. The textbooks I use just touch on vectors for a few sections.

[@profrobbob]

Thank you for "liking" my video....and I appreciate that you found my channel and decided to tune me in!!! I hope you continue to watch and learn and please share my channel with your friends...thanks:)

[@profrobbob]

That's awesome news Travis! Look at the positive side...you can learn from me anytime you want, you can fast-forward and reverse, "you" can make the choices...and this way I can continue to help others just like yourself, all over the world at the same time:) Thanks again for your continued support.

[@PawanABudhwani]

thank you so much sir your enthusiasm to teach the maths subject is very nice I am really thankful to you for teaching maths .you are very very very very very great. thanku so much.

[@tunneltrance]

This video is really helping me with my Physics summer class, thank you! (It's a 5 week class so the professor really can't give in depth concept explanations). I hope all of your close captioning is going well so you can start making videos again soon :)

[@profrobbob]

Glad it's helping...please share this resource with your classmates and teacher for all the future students too:D The CC I was doing was temporarily put on hold las school year since I had 4 preps to plan for, same with not having any spare time to even make many new videos:( As you know, I reached out to my KZbin community but only had a small amount of follow-thru. Was hoping someone would see my plea and have the means to finish them all!...but I'm not giving up. I'm going to try to make some more Calc videos over summer break...we'll see. Thanks for watching and please keep sharing whenever you have the opportunity...help may still be out there!

[@kiranmehr4118]

THANK YOU THANK YOU THANK YOU!!!! You have saved my butt as for my grade and the finals! :) Can always depend on you! Hats off, Good Job :)

[@profrobbob]

+Kiran Mehr You're welcome...thanks for taking the time to study, like and sub to this free educational channel and I hope you will tell all your class and teacher about it, tell them how it helped and please watch and do the same to help us keep growing:D

[@georgesadler7830]

Professor RobBob ,thank you for a great Introduction to Vectors. Vectors has many applications in real life. Vectors also appear in Precalculus, Calculus III, Engineering Physics I, II, Statics, Dynamics plus advanced courses in Engineering and Physics. There is a minus sign missing on the a 1 plus a2 I component.

[@cachietsao6507]

Tarrou, your chalk writing is so beautiful, I'm gonna mimic it ;) , and of course, the content is very helpful and interesting. Thank you!

[@profrobbob]

AWESOME Cachie Tsao You're welcome and thanks for watching, liking, subbing and mimicking...which they say is the greatest form of a compliment:) Please share my channel with your friends, class and teachers too:D

[@IK-np7we]

Another great lesson! Thank you so much. Now, I think I am ready for my calculus I.

[@profrobbob]

You are very welcome...and THANK YOU as usual for watching and supporting! Now go into that Calc class with confidence and help the teacher teach...BAM!!!

[@MrSpander]

thank you your videos have helped me tremendously, my online trig instructor is not as inspirational about helping as you are. thank you.

[@profrobbob]

Do have the answers? I think there is two vectors. The (3,7) vector make a 66.8 degree angle with the x axis or horizontal and you want a vector of length 4 to have 40 degrees between it and vector u...so it could be a vector with 26.8 degrees to horizontal. If you set up a right triangle with a horizontal leg, angle of elevation of 26.8 with hyp of 4 the hor component is approx 3.57 and vert is approx 1.8... I think:)

[@profrobbob]

You're welcome...and THANK YOU for supporting by liking and subscribing, I really do appreciate the support!

[@najiyahkhanom8611]

3 mins in and it already makes sense

[@profrobbob]

BAM!!!

[@profrobbob]

Thanks for the compliment!

[@profrobbob]

I'm was going for the GOLD...looks like I made it!...LOL Thanks for watching and please spread the word to any future online friends. Thanks for watching:D

[@Chozen_afitra]

needed serious help in this and God led me to you , thanks soo much

[@profrobbob]

You're welcome Richard Muchogu Please take the time to like and SUBSCRIBE and then tell all your friends, class and teachers to do the same and keep sharing my channel to help us groW!

[@aditimajumdar2459]

wow!!!!!THANK YOU so much sir.....now the concepts are crystal clear to me👌😁😊😊

[@profrobbob]

Love to hear it...that's when I normally shout out...BAM!!!

[@aashsyed1277]

wow such a unbelievable!!!!!!!!!!!!!!!!! this is like 1000x better than my professer WOW! thank you!

[@profrobbob]

Thank you Aash. I threw in everything but the kitchen sink into this lengthy introduction of vectors years ago. Glad you are still finding it effective😊

[@alonsoferna6953]

Thanks for sharing, needed help before examination .. thanks alot...!!!

[@profrobbob]

Absolutely:) If you watch my video about "setting up the unit circle", explain how the concept of similarity along with the two special triangles (30-60-90 & 45-45-90) are what make 12 of the ratios/coordinates around the unit circle. Only the quadrantal angles are not found using the special triangles. Sorry I rambled on too long in the beginning of this video. I made this not long after my time limit was lifted. You can help by telling others about my channel and watching/clicking the ads

[@profrobbob]

Thank you very much for helping me:):):) I added in the missing 2 with an annotation...unfortunately iPads and iPhones won't see the annotation correction.

[@liteshrao8508]

Sir, I have already done series of calculus courses followed by ODEs and PDEs, Linear algebra and other next sequence of courses. It seems that you can help other students like me who just attend classes and forget most of the concepts after one or two year of the course because your classes have deeper understanding of the concepts. Through this medium, I am requesting you to please, if you can, upload you lectures on advance mathematics subjects as well like numerical analysis, functional analysis, real analysis etc. I believe you can do wonders in maths education

[@profrobbob]

You would draw vector a with the same length and direction as given...in my example up and to the right. Then go back to the initial point and draw vector b going to the left (the opposite direction of the given vector). Your parallelogram will be drawn up and to the left. I hope this makes sense. Thank you so much for still watching!!!

[@gloriazhang1998]

Thank you so much honestly i would be failing without you

[@profrobbob]

You're welcome Gloria...but remember, YOU were the one who took the time to find me on KZbin, I was lucky that you choose my channel to learn from and subscribe to:) Keep up the good job studying and I hope you will share my channel with everyone looking for free math help!

[@profrobbob]

THANK YOU for supporting by subscribing! My mission is to show that math can be fun while learning...I do take teaching very seriously but strive to make the learning experience enjoyable. I hope some of my enthusiasm will rub off and help you enjoy learning math:D

[@profrobbob]

I don't remember exactly how I discussed the 30-60 triangle here but that is how I introduce working with them in my math class. Thanks for the comment and watching my video:)

[@zhangwinni]

this is so helpful, I cant even.. thank you SO mcuh for doing what you do, its greatly appreciated!

[@nemoyrosy]

haha i like your videos man. at 21:50 did you said " any ray"? haha. i heard any ray. keep does videos coming. i have told my entire classmates to watch your videos. I hope you get more popular because you're a great teacher.

[@profrobbob]

"at any rate"...those were early videos filmed in a very large classroom, maybe it was the echo:) ...any ray (lol)...thanks for watching, liking, subbing, and sharing with all your classmates. I really appreciate all the support and the nice compliment from you and hope you continue to enjoy your learning experience from Tarrou's Chalk Talk nemoyrosy !

[@stevenoverton8316]

It's true isn't it? Trig really IS a deceptively simple subject. You certainly make it accessible. Thanks.

[@profrobbob]

It can be when it clicks:) Thanks for watching and subbing...please share this free resource with everyone and share it on social medias for others to discover too...BAM!!!

[@profrobbob]

Even though you are probably working with any angle and not just the unit circle angles, I think you would get a lot out of my two videos Setting Up the Unit Circle part 1 and part 2. I explain where the values come from, the sign changes of x and y in the different quadrants, and explain and set up reference angles and reference triangles form many different angles.

[@mitchjvb]

Very nice video! One thought... with trig ratios of 30-60, consider finding the side lengths using ratios, such as x,2x,x root3. Otherwise, I think this video will be easy to follow for students with a good Geometry foundation. Have a great day!

[@ghostfrom1950]

This IS A- MAZING!

[@profrobbob]

THANK YOU! I made a lot of vector lessons at the beginning of the school year. Check out my playlist link in the description.

[@profrobbob]

Keep studying and keeping those A's coming...and then the next one is sure to be an A+...BAM!!!

[@harrys.5052]

I wish you were my teacher. You do a great job and are very engaging! How many math degrees do you have by the way?

[@profrobbob]

You're welcome Shane:)

[@ri438j]

Awesome job. Not too far in the future I expect I will be learning more online than I can in the classrooms! Just a note though... Faster is better because its easy to just rewind if the concept wasn't clear the first time. Don't overdo it professor.... Save your energy! And ooh yea.... lose the red chalk please... we can't see it clearly. Thank you for all your doing and am looking forward to more interesting lessons!

[@Erin-bc8ic]

Very good video, thank you so much!

[@profrobbob]

+Eric M you're welcome, thanks for watching!

[@zaryaomer2739]

You are a treasure man masha allah

[@profrobbob]

Thanks for watching!

[@profrobbob]

And THANK YOU so very much for choosing my channel to learn math from! Please share my channel with your friends too:D

[@ahmedalkarkhi]

the best math video on vectors !! :D

[@jakemondares1453]

You’re great in explaining the concept. Thanks a lot!:D

[@inovexa4039]

a god .. no other words u are a god .......

[@profrobbob]

Thanks for your continued support!

[@jordanishi4]

@ProfRobBob "End to End" I've seen it labeled the "Tip to Tail" method.

[@amanial-khalifa5299]

thanks for sharing

[@profrobbob]

You're welcome:) I already have one, you can find it under "ProfRobBob"...(I set everything up the same in the beginning thinking it would all be easier to find that way:) Thanks for caring!

[@habtamutassew2981]

very interesting .......i like the way you teach!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!1

[@profrobbob]

+habtamu tassew thanks for watching, liking and subbing...please share your interest and my channel with all your friends, classmates and teachers too:D

[@Mutubeish]

Hellllo awesome video, watch it a few times now.. i got a question on that last part. shouldnt it be [if "a" is = 18 ] -----> √a = 4,24 ????

[@profrobbob]

HAHA... This video is WAY too long. I broke out two parts and posted shorter videos with them. I got too excited about having my 15 minute limit lifted:D I will reshoot this video when I teach vectors next year...probably.

[@HERKFOOT21]

As you can tell i commented on a lot of these trig video bc my proffesor was not a good one, my whole class had trouble but you helped me pass, i learned about 90% of trig from you and i went in know nothing since i didn't trig in HS but i was able to pass this semester thanks to all your videos (about half your trig views are from me btw). Also i will continue in all my calculus classes to view your videos! I do have one question, since it's summer i wanna prepare and try to get ahead in pre calculus, is pre calculus kinda a review of trig or will there be a lot more new things? thanks again for all your help!

[@profrobbob]

HERKFOOT21 If you have a really good Algebra 2 foundation like the students I get at my high school, then PreCalc should be mostly a fast paced review of Algebra 2 with three chapters of Trig that are mostly new. If you have already had Trig, then the entire year/semester will be a faced paced review with sprinkles of new material. The last chapter of PreCalc will be the only new chapter giving you a preview of the first chapter of Calculus. Thank you for being a long time viewer and subscriber again:D We really appreciate it. Now...on to get that A in PreCalc and then Calculus 1! BAM!!!

[@Eddierocket2010]

thanks for this video. what is the next step up from this? i am really stuck on vectors but in scenario type questions involving either force or speed. have you got any videos that covers different types of vector questions? thank u so much for these, u r a great guy for sharing these. much love from liverpool uk

[@profrobbob]

Eddierocket2010 Try this lesson kzbin.info/www/bejne/aZebn5pmq7qeeqc&feature=youtube_gdata&list=PL4FB17E5C77DCCE69 Thank you for watching and your kind words. Glad I can help:D

[@profrobbob]

Thanks:):):)

[@BboyDaquack]

Thank you so much! my professor really confused me here. subed/liked!

[@mamu7mich]

could you tell me the difference between the reference angle and the direction angle? when taking the x and y components which one should we use? the reference angle or the direction angle?

[@profrobbob]

I take it v is 4 units long?

[@medicineman1202]

I've decided to skip class and just watch your videos as I find them more informative and comprehensible.

[@PMJS15]

please teach my professor your ways lol

[@shivamdewan3448]

Same

[@vineetdeepika]

Sir, In the parallelogram notation , you showed vector b - vector a as a diagonal of a parallelogram . But how do we show vector a - vector b from the same initial point as vector b - vector a?

[@MrSpander]

oh shoot, you are awesome sir. I thank you sooo much!!

[@stealthmintblue]

Thank you sir! Great vid! BAM!!

[@priyashasinha170]

this was amazing!!!!

[@kshitizlakhotia1318]

It was amazing Thanks

[@dpmike32819]

The short leg of a 30 60 90 triangle is half the hypotenuse and the longer leg is the short leg times the square root of three. Theorems from geometry

[@Alungo999]

In the End to End method, how do you know in which directions to draw the vectors?

[@wuttupg]

Hey Torrou! Around minute 38, you wrote the answer for "a" (on the triangle itself) as sqrt of 3 instead of 2sqrt3. :D Just letting you know cause I know you like to fix those little errors.

[@mamu7mich]

I always get confused as to what the value for theata be when we are calculating x and y components. in the second co-ordinate when the angle is given with respect to y axis. can we use reference angle here? i.e 180- (that angle) and what about other co-ordinates. And btw what's the difference between the direction angles and the reference angle? in an other case when the angle is in 3rd co-ordinate with respect to x-axis can we use reference angle here? i.e (that angle) -180? please reply !!!

[@mamu7mich]

thank you. By the way, I suggest making a facebook page. That way you can be more connected to your fans.

[@kelseyshelton132]

Thank you so much!!!!

[@profrobbob]

+Kelsey Shelton you're welcome so much and thanks for liking, studying and subbing too!

[@ServitorSkull]

32:15 I see that that magnitude of vector v was calculated to be 5. What about the -5 since that was the result of a square root? I see these negative values constantly being thrown away. Will this continue with vectors or can there be negative vectors? Or are those vectors just going the opposite direction?

[@profrobbob]

Magnitude is a measure of length and therefore cannot be a negative value. A "negative" vector is simply an opposite vector with an opposite direction.

[@HYPEREXTREAME]

I'm good at math! nice t-shirt :D