Dot Product and Force Vectors | Mechanics Statics | (Learn to solve any question)

[@aryamhaske7307]

I am a first year engineering student. your videos make statics and dynamics of mechanics so much easier and intuitive. This is the toughest subject for me to study because proceeding in these problems isn't very "natural" to me, but i felt sooooo relieved when i found your channel .... really good content, and i can't thank you enough for your help in uploading these videos for free.

[@QuestionSolutions]

I’m thrilled to hear that you’re finding the videos helpful in your studies! It’s always rewarding to know that the content is making a difference. Remember, it’s perfectly normal to find these topics tough at first, but with consistent practice and study, it will become more intuitive. Keep up the great work!

[@PunmasterSTP]

How's engineering been going?

[@rababalsadah3037]

you just saved me from failing my statics course. Thank you!

[@QuestionSolutions]

You're very welcome! Keep up the good work and best wishes with your studies.

[@sphephelohlophe8086]

I watched your content before going to write my exam , The result are not back yet and the level of confidence i have is way to high. Your videos helped me a lot thank you brotherman🤝

[@QuestionSolutions]

I hope you did great on your exam! Thanks for taking the time to write a comment like this, it's really nice. Keep up the great work and I wish you the best in your future endeavors.

[@sphephelohlophe8086]

@@QuestionSolutions Thank you. And I hope you continue making us great content in the future🤝

[@cobragaming1272]

thanks a lot, i got 100% marks in my mid exam in statics

[@QuestionSolutions]

NICE!!!! I am really happy to hear that. Thanks for taking the time to let me know :) Keep up the awesome work

[@edran4449]

u sound like the organic chemistry tutor, and u explain just as well him, r u him?

[@QuestionSolutions]

No, I am not 😅

[@ChalaBona-rm9qr]

Honestly better than organic chemistry❤

[@Hadron11112]

Hi sir I have a question, in your previous video called “force vectors along a line | learn to solve any question” at 5.47 you find the magnitude of the force from the Cartesian by doing the square root of the 12 squared, the 9 squared and the 8 squared to find the mag then times this by the unit vector to equal the force. And I don’t understand why we don’t use this same concept at 3.34 where u times the unit vector not by the magnitude but by the different components of force F to find the force along the cables.

[@Hadron11112]

Is it because in this example we have 2 cables instead of one? I still don’t really understand, thanks for any help

[@QuestionSolutions]

Here, this question is related to projected components. We are given a force expressed in cartesian form and we are told to figure out the projected components of that force along each cable. So we use a different method. The process is pretty much the same as before, but instead of multiplying a scalar force value by the unit vector to get a cartesian force, we are already given a cartesian force so we take the dot product between each component and the unit vector. So in other words, we are getting a scalar force value for each cable. We aren't expressing it in cartesian form.

[@fromiraq3451]

Thank you so much❤ From Iraq🇮🇶

[@QuestionSolutions]

You're very welcome! ❤

[@mohammadshabih5293]

finnaly a good statics teacher on youtube

[@QuestionSolutions]

😅 Many thanks!

[@abdullaheminbilgili351]

you are best teacher i ever seen thanks

[@QuestionSolutions]

Wow, thank you! I wish you the best with your studies.

[@Poindexters-Obsession]

For the problem at 2:30, how do you rectify the forces between the two cables with both carying some portion of the applied force? Did I miss how you balanced all the forces? The calc appeared to place the entire force on each cable independently to me.

[@Poindexters-Obsession]

Should the cable force magnitudes multiplied by the cable unit vectors sum to equal the applied force when comparing the components?

[@QuestionSolutions]

@@Poindexters-Obsession It seems like you're confusing projected components with force vectors along a rope/line. Please watch this video first: kzbin.info/www/bejne/eXTIiKxnoNKrg9U

[@eve422]

So easy to follow and clear. Thank you so much!

[@QuestionSolutions]

You're very welcome! Glad to hear it's easy to follow👍

[@astridahmushili1305]

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[@QuestionSolutions]

You're very welcome!

[@marnis_antonites]

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[@QuestionSolutions]

You're very welcome and I am glad these videos are helping you :)

[@cautiouscactus6999]

im glad i found your channel ❤

[@QuestionSolutions]

Thank you so much. I am glad you're here watching these videos! ❤

[@darrylcarter3691]

In example 2, I heard you say the the negative sign means that the components points in the opposite direction of the unit vectors. The way I observed the picture, and based on the problem I solved, it seem like we can think of as the vector for Force AB pointing towards point B, and the vector for Force AC pointing towards point C.

[@QuestionSolutions]

Yup 👍

[@FreeFire-il4vw]

5:13 what made u said its the parallel vector ? How to identify whether it is parallel or perpendicular? Please can you ellaborate...

[@QuestionSolutions]

Watch again from 0:25. Taking the dot product between the force and the unit vector gives you the parallel component.

[@FreeFire-il4vw]

Thank you

[@QuestionSolutions]

You're welcome. Once you have the parallel component, you can get the perpendicular component easily. ​@@FreeFire-il4vw

[@canyoldascayl2247]

so impressive.. thanks for a good video my teacher

[@QuestionSolutions]

You're very welcome! Best wishes with your studies.

[@s7lb384]

YOU ARE THE GOAT!!

[@QuestionSolutions]

Thank you!!

[@uchiha_kakashi6716]

3:32 why we need to multiply F with uAB and uAC

[@QuestionSolutions]

Please see 0:33. We are doing the same thing, taking the dot product. The only difference is, instead of it being about an axis, we do it about a specific cable (in this case, that is our axis).

[@kevins8314]

This was an awesome explaination!

[@QuestionSolutions]

Glad to hear! Thank you very much.

[@axviiaxvii5909]

So whenever a question states "projection", you have to calculate the unit vector?

[@QuestionSolutions]

Yes, pretty much at some point, you will need to have the unit vector.

[@PunmasterSTP]

Dot's another great video!

[@QuestionSolutions]

😂

[@mamba5075]

5:37 Can we find perdendicular force in vector forms

[@QuestionSolutions]

The dot product results in a scalar value.

[@davidespejo7255]

You make all this look so easy

[@QuestionSolutions]

Haha, glad to hear :)

[@morgan9992]

wow wow wow , thank you so so much . you are the best

[@QuestionSolutions]

You are very welcome!

[@DaHoKilla]

Amazing video thank you

[@QuestionSolutions]

Thank you very much!

[@mitchellemavesere7563]

Thanks very much it's helping a lot

[@QuestionSolutions]

Glad to hear :)

[@nomthethomaseko1833]

i can't thank you enough

[@QuestionSolutions]

You're very welcome!

[@roenroderio3844]

At problem no.2 won't the sum of forces from vector components of AB and AC be equal to F?

[@QuestionSolutions]

Yes, it would, but keep in mind, FAB and FAC values we found were scalar.

[@edran4449]

kinda wished i knew about ur vids at the begining of my semeter, cause 2day is my test and i started watching 2day, im screwed with the little time i hav left

[@QuestionSolutions]

Give it your best shot! I wish you the absolute best on your test.

[@basakakn6806]

lol im in the exact same position a year after

[@Hussain-e9z]

Why do you need to find the unit vector in example 2 but not in example 1?

[@QuestionSolutions]

In example 2, it was a force along a line, (the ropes/cables).

[@naamanmwela7219]

you are the best thanks

[@QuestionSolutions]

Many thanks!

[@basavarajgl5453]

thank you😍🤩

[@QuestionSolutions]

You're very welcome!

[@ibrahimhashmi6716]

How can we find the Cartesian form of the perpendicular component?

[@QuestionSolutions]

Please kindly give me a timestamp so I know where to look.

[@Carusot]

Can i write cos(theta)=rAB(bold)*rAC(bold)/rABrAC as for example: cos(theta)= A(arrow)*B(arrow)/AB

[@QuestionSolutions]

Are you writing position vectors? You have to use the letter "r" to represent a position vector. So instead of bold, you can write rAB with an arrow on top. See: en.wikipedia.org/wiki/Position_(geometry)

[@Carusot]

@@QuestionSolutions yeah thats what i was trying to ask haha, hard to write mathematical equations on youtube. just what you write as r(arrow) i got confused with the difference compared to using just vectors ("a" arrow), i think i get it and try to remember r as a reference for where a force is in a space (starting in a certain point o) and the vectors a or something as just vectors telling you your direction in space? Thanks

[@QuestionSolutions]

@@Carusot That is correct. I have a short video on position vectors, if you have time, please take a look, it might help you out: kzbin.info/www/bejne/eXTIiKxnoNKrg9U

[@Carusot]

@@QuestionSolutions You don't know what it means to students when you actually respond even after 2 years... Whenever you think its pointless and useless please don't stop because it really helps people alot so they can continue on.

[@Carusot]

@@QuestionSolutions What got me confused and is very confusing, we use AB(->) not rAB. So after one year i was looking at this rethinking my life. Why is it used in different forms tho?

[@ahrya3148]

thank you bossman

[@QuestionSolutions]

You're very welcome!

[@jiayuzhang9681]

Hello, for question 3, how do we know that the result of 99.5N is parallel? Thanks!

[@QuestionSolutions]

That's sort of the whole point of going through the dot product. 😅

[@vek5661]

why didnt u make it unit vctor for example 1

[@QuestionSolutions]

So you have to look at the equation to get the angle (shown at 2:15). Notice how it doesn't require any unit vectors, just the position vectors.

[@NK-iy6if]

For the 3rd example why is B=-1.5i+2j+2k why is it not B =-1.5i +2j-2k

[@QuestionSolutions]

For it to have a negative k component, it needs to be below the x-y plane, in other words, point B must lie on the negative z axis, but its above.

[@pyroad23]

I had the exact same question and I got the same answers as you but my prof m asked my answer for parallel wrong and said it should be 82.4N. A

[@QuestionSolutions]

I don't know which question you are referring to. Please use timestamps so I can take a look, thanks!

[@pyroad23]

@@QuestionSolutions it was the third questions 3:45

[@QuestionSolutions]

I am not sure, but the answer shown is correct. Maybe your professor had different values? Not sure :/@@pyroad23

[@funky2964]

How did u got 5?

[@QuestionSolutions]

The 5.099? It's the magnitude of rAC. So you take each term, square it, add it all together, and then take the square-root. See: kzbin.info/www/bejne/eXTIiKxnoNKrg9U

[@saiprasadsatya3677]

What exactly unit vector means

[@QuestionSolutions]

Please see: kzbin.info/www/bejne/eXTIiKxnoNKrg9U

[@nimcaandayib6222]

Point C:(3i+5j+(0k)?)m Teacher z is not zero, it exista How does the Z became 0k?

[@QuestionSolutions]

Please use timestamps so I know where you're talking about. Also, z is zero because point C lies on the floor, which means z=0.

[@nimcaandayib6222]

@@QuestionSolutions thanks dear teacher .I worried alot about statics but When I get this channel ,statics become easy.

[@QuestionSolutions]

@@nimcaandayib6222 Glad to hear :) I wish you the best with your studies!

[@Devinci297]

for BD I have The j component is -4 Never mind, It's D - B. I'm stupid!

[@QuestionSolutions]

You're not stupid, mistakes like that are easy to make and happens to everyone :)

[@Devinci297]

@@QuestionSolutions Thanks for the amazing videos!!

[@QuestionSolutions]

@@Devinci297 You're very welcome!

[@josephluzon6391]

2:24 the angle is 1.29😅

[@josephluzon6391]

Ah i get it now u solved the magnitude 1st before you put it on the equation (3.6055)(5.099)=18.38 Then Cos-1(5\18.38)

[@QuestionSolutions]

Yes, that's why it's all included in a bracket. You can just plug it into your calculator directly and get the angle in degrees.@@josephluzon6391

[@pubgmemer1478]

why didnt i found u earlier

[@QuestionSolutions]

Better late than never :)

[@mouhmdmouhmd8623]

اخي هل تعرف تتكلم عربي لدي اسألة كثيرة

[@QuestionSolutions]

I don't know what you said, sorry!