The Vector Cross Product

  Рет қаралды 871,707

Professor Dave Explains

Professor Dave Explains

Күн бұрын

Пікірлер: 338
@chenchoon8751
@chenchoon8751 4 жыл бұрын
Why can't my university prof just put up these videos and call it a day. That way I won't be binge-watching these videos the day before the test
@ConceptualCalculus
@ConceptualCalculus 4 жыл бұрын
You do know how to find them. Nothing is stopping you from watching them earlier than the day before the test.
@yugagalaxa98
@yugagalaxa98 4 жыл бұрын
Y'all are studying this in uni?
@chenchoon8751
@chenchoon8751 4 жыл бұрын
@@yugagalaxa98 Yeah!
@chenchoon8751
@chenchoon8751 4 жыл бұрын
@@ConceptualCalculus Woah man you might have a point! Thanks for pointing that out idk what I'd do without you!
@yugagalaxa98
@yugagalaxa98 4 жыл бұрын
@@chenchoon8751 oh. We study it in 11th grade...
@81brassglass79
@81brassglass79 4 жыл бұрын
Hey professor Dave! you are my hero and I would love to be as cool as you someday. It tickles me the way you combat flat eathers while also helping me learn the material my engineering professors can not. You have made my school life much better since i have stumbled upon your videos and i can not thank you enough. Please keep up what you are doing and know that you are a more than a professor you are a HERO!
@seidahmed1580
@seidahmed1580 3 жыл бұрын
I would completely agree....i feel my highschool year has been easier since i found u❤️
@andreamalaver6155
@andreamalaver6155 2 жыл бұрын
this man is single handedly saving my engineering career 😭
@ren-cf2fq
@ren-cf2fq 8 ай бұрын
us 😭
@Sam-em9zy
@Sam-em9zy 5 ай бұрын
Omg samee here 😭🥲
@iocallisto69
@iocallisto69 5 ай бұрын
@@Sam-em9zy im not a uni student, but the way everyone in these comments sections describe uni, Im cooked
@andiswamanqele794
@andiswamanqele794 3 ай бұрын
Him and The Chemistry Tutor guy🔥
@youcefkartobi3436
@youcefkartobi3436 Ай бұрын
same bro😂😂
@nhaz652
@nhaz652 2 жыл бұрын
Hello. I have a qn on Vector Cross Product. 1) Is there a reason why we have to subtract first followed by adding the next vector? 2) Is there an order as to whether or not I should take -5 x 3 first, and then 7 x 4? 3) May I confirm that in each of the vector after solving its multiplication, I have to subtract it? For example, (-5x3) - (7x4)
@carultch
@carultch 2 жыл бұрын
Multiplication of ordinary numbers is commutative, but this is not the case for the cross product. For the cross product, a cross b is not the same thing as b cross a, because a cross b is the negative of b cross a. You can multiply the individual numbers in any order you want, that carry out the cross product. But to set up the multiplication, you need to keep the vectors in the correct order.
@C_H_R_O_L_L_O
@C_H_R_O_L_L_O 2 ай бұрын
1) yes firstly we took + sign because of the position of that i cap i.e; a11 (1+1=2)(even) so positive then j cap belongs to a12 (1+2=3)(odd) so negative and so on... 2)That's the way of doing determinants 3)that's the whole way of solving determinants
@kironblackwood3004
@kironblackwood3004 4 жыл бұрын
I've come across your videos just recently and am so happy I did; thank you SO MUCH for you crystal clear understanding of these concepts!!
@danieljulian4676
@danieljulian4676 5 ай бұрын
Cross product: (1) Only in 3D space (2) the value of a determinant is defined to be a scalar quantity, not a vector; the rubric for the cross product is only a mnemonic. Do not study only with this channel unless you wish to treat it simply as prep for exams that will include only very rudimentary "calculate this and give us a number" exercises. In other words, you're not learning linear algebra from Professor Dave in any depth. It's quick, thorough prep for next day's exam if you're only asked to calculate.
@merry3755
@merry3755 2 жыл бұрын
Mate, thank you so much for these videos, I wouldn't have been able to pass my midterms without you.
@kaomaphiri7749
@kaomaphiri7749 3 жыл бұрын
3 years later I'm watching this and it still explains it so easily. Keep it up 😊😊😊😊
@rajyalaxmik6690
@rajyalaxmik6690 4 жыл бұрын
My Sir explained this topic many times but I couldn't relate, when prof. explained understood very clearly ...Thanks...
@junaidfazlani04
@junaidfazlani04 Жыл бұрын
I had been struggling for several months with cross products. I never thought your explanation could help me clear the topics smoothly! Thank you so much professor dave
@anpanmanhope3977
@anpanmanhope3977 3 жыл бұрын
You're a life saver Professor Dave !
@sukritbera5244
@sukritbera5244 4 жыл бұрын
Thanks prof, I passed the physics paper with ur help.....ur tutorials are awesome
@sachindhakal2716
@sachindhakal2716 3 жыл бұрын
i just want to learn vector cross product to find area of triangle but as i opened your channel i found ocean of knowledge .omg im shocked...thnak you so much prof deck from this learner from nepal
@cherinhalechantry8786
@cherinhalechantry8786 4 жыл бұрын
Very clearly explained! Thank you Professor Dave!
@lingwaili1203
@lingwaili1203 2 жыл бұрын
Thank you, professor Dave! English is not my mother tongue but I understand Linear Algebra better than I am learning in my university
@gka_renaca
@gka_renaca Ай бұрын
I used to watch him as I studied for ap's now I watch him at Stanford. thank you goat
@sirtristram8297
@sirtristram8297 29 күн бұрын
Resolve b into two perpendicular components, one parallel to a, and one perpendicular to a; then: magnitude of cross product = [magnitude of a] X [magnitude of the component of b which is at right angles to a (which is "b sin theta") ]
@memeingthroughenglish7221
@memeingthroughenglish7221 Жыл бұрын
You're currently my favorite math KZbinr!
@Saisenpai991
@Saisenpai991 3 жыл бұрын
Thank you so much sir your explainations are superb and works like a one shot before exams.... By the way, love from India ❤️
@Pang-z5i
@Pang-z5i 2 жыл бұрын
professor Dave is just the best. Now are understand more about the topic
@zacharineemi
@zacharineemi 6 жыл бұрын
Nice tutorials. It helps me alot.
@TheZMasterful
@TheZMasterful 6 жыл бұрын
@@RajKapoor-ix4mk sum indian ned pusi
@laithdarras6389
@laithdarras6389 10 ай бұрын
Make sure you put the arrow above to indicate that it's a vector!
@seemasatheesh6424
@seemasatheesh6424 5 ай бұрын
This man is saving LIVES 🙌🏻
@kanivakil198
@kanivakil198 4 жыл бұрын
2:23 right-hand rule
@skm2
@skm2 2 жыл бұрын
i such love the introduction of this channel it is so shiny
@SeriousStudent603
@SeriousStudent603 2 күн бұрын
2:00 vector : CROSS product (vector. like finding determinants) . not DOT product (scalar). 2:55 direction of cross product. a x a = 0. 4:00 magnitude / length of vector. parallel vector cross product = 0. 4:15 4:40 . 5:25 cross product only follows distributive property.
@varshinilolla3090
@varshinilolla3090 3 жыл бұрын
Thanks for the video! In comprehension, a×b= -3i + 19j + 10k So, |a×b| = √(-3)^2 i + (19)^2 j + (10)^2 k = √470 Is √470 = |a| |b| sin⊙ ?
@small_ed
@small_ed 3 жыл бұрын
Excellent presentation with explanations that get right to the point.
@kungfupanda5491
@kungfupanda5491 2 жыл бұрын
PROFESSOR YOU ARE TRULY THE BEST. LOVE YOU, FROM KENYA
@ConceptualCalculus
@ConceptualCalculus 4 жыл бұрын
Hi Dave. I love your videos. Since we all went online abruptly, I have been using them a lot in my classes. Thank you.
@TrendCast314
@TrendCast314 2 жыл бұрын
Thank you professor dave, I hope i pass my exam later. You are very helpful!!
@Melpomenex
@Melpomenex 2 жыл бұрын
did you pass?
@arvindpawar9243
@arvindpawar9243 3 жыл бұрын
because of ur teaching i got excellent marks in this chapter thank you sir thank u very much......
@alusandrea1501
@alusandrea1501 Жыл бұрын
This is way easier to understand than memorizing a formula.
@AbdouMessaoud
@AbdouMessaoud Ай бұрын
You are the best in the mond bro
@sylabelleambourouet1151
@sylabelleambourouet1151 Жыл бұрын
Wow🎉🎉 I really love your way to explains, it's so easy to understand clearly. Thank you so much
@wesselbeer8041
@wesselbeer8041 Жыл бұрын
i have an exam tomorrow. this is a great crash course
@blenderup6223
@blenderup6223 Жыл бұрын
I have mine tomorrow as well
@bernab
@bernab 5 жыл бұрын
Why a x b as a result is 19 j positive? I think is -19j
@giacomodoppiazeta8069
@giacomodoppiazeta8069 5 жыл бұрын
The second coordinate (j) is the negative of the multiplication. Basically, once you have your result, you just negate the second coordinate. Check 03:22
@MrChesemis
@MrChesemis 3 ай бұрын
I LOVE EDUCATION KZbin THANK YOU SO MUCH PROFESSOR DAVE, YOU ARE A STEPPING STONE TO MY CAREER AS AN AEROSPACE ENGINEER. Sorry I really love science.
@louismiranda2850
@louismiranda2850 7 ай бұрын
Could you do a playlist on dynamics?
@ProfessorDaveExplains
@ProfessorDaveExplains 7 ай бұрын
check my classical physics playlist
@Ligtaau-xj3oc
@Ligtaau-xj3oc 2 ай бұрын
you always make me feel physics is easy
@meera7572
@meera7572 3 жыл бұрын
dude u are greatt you are freaking great i wish indian schools would have teachers like you!!!
@rslitman
@rslitman 2 жыл бұрын
Why isn't the Vector Dot Product video not in the Linear Algebra playlist?
@LA-cm9uo
@LA-cm9uo 2 жыл бұрын
I learned more from this video than what I learned during my entire degree
@XOR-lith
@XOR-lith 4 жыл бұрын
Came for the flat earth wreckage, stayed for my Master's degree.
@carultch
@carultch 3 жыл бұрын
Well I guess that's one advantage of flat Earthers existing. Getting you introduced to people like Dave to help you earn your degree.
@SantoshKumar-ie5nm
@SantoshKumar-ie5nm 3 жыл бұрын
Thanks sir ur vedios are short and very helpful🙂🙂🙂
@yaluman.
@yaluman. 3 жыл бұрын
Thanks man I have exam tomorrow and I understand it
@adarshthorat7179
@adarshthorat7179 3 жыл бұрын
Thank you sir☺️☺️ Love from India🇮🇳🇮🇳♥️
@hitler-chanofficial8483
@hitler-chanofficial8483 3 жыл бұрын
Bobs and vegan (ʘᴗʘ✿)
@spidystrac6218
@spidystrac6218 3 жыл бұрын
I am from India.... State :telangana
@sarahelana535
@sarahelana535 5 ай бұрын
Is the cross product a resulting vector? Or is that term only used when adding vectors?
@lilsatsworld8878
@lilsatsworld8878 4 жыл бұрын
Great sir, i understood concept very well . Thanks for being there sir
@rendagostino675
@rendagostino675 Жыл бұрын
saving me at 1am the night before my mid semester
@sitasiktapurohit1447
@sitasiktapurohit1447 4 жыл бұрын
Thank god i got this video... thank you sir....
@muhammedbayram4624
@muhammedbayram4624 4 жыл бұрын
Very clear,thank you.
@Syntaxxed
@Syntaxxed Ай бұрын
at 5:37 are a,b and c all vectors (in the distributive property)?
@LifeLise
@LifeLise 8 күн бұрын
Yes.. parentheses first, so if you add vectors b and c the result is one vector (b+c), therefore you can find the cross product between the two vectors a and (b+c)😊
@almahdiabdulkarem1735
@almahdiabdulkarem1735 4 жыл бұрын
U r the best professor Dave, thanks
@gabygaray7304
@gabygaray7304 2 жыл бұрын
Do you have a video like this for addition with the same amount set of numbers?
@shendhaneravi6636
@shendhaneravi6636 2 жыл бұрын
at 6:00 *a x b* is (27 i + 19 j + 10 k) and not (-3 i + 19 j + 10 k)
@Waltu0
@Waltu0 2 жыл бұрын
When I included the negatives : (-12-15)i-(24-(-5))j+12-(-2))k , I got -27i-19j+14k.
@lukendorf511
@lukendorf511 11 ай бұрын
Great explanation, thank you!
@DeepeshSachan
@DeepeshSachan 7 ай бұрын
So any advices for electrostats ?😅
@jaswanthreddy-jk1bq
@jaswanthreddy-jk1bq Жыл бұрын
it's such a wonderful session thank you, sir!!
@jerelynbarrientos2064
@jerelynbarrientos2064 Жыл бұрын
you explain so well! thank you!
@nathaliamesquita6740
@nathaliamesquita6740 3 жыл бұрын
Well, that's the fastest I understood anything in linear algebra
@trishatalaroc2968
@trishatalaroc2968 3 жыл бұрын
I do have a question about this part 1:51. How come the answers of 4x7, 4x2, and 3x2 are all negative? Is it always negative when in fact they are all positive?
@jursamaj
@jursamaj 3 жыл бұрын
That's the way the determinant of a 2*2 matrix is defined: [a b | c d] is ad-bc. So the one that is [3 4 | 7 -5] above yields 3*5-4*7.
@republicofprogaming785
@republicofprogaming785 3 жыл бұрын
Professor Dave!!! Every thing is perfect except the audio. Please be loud!!!!
@vandanareddy5780
@vandanareddy5780 2 жыл бұрын
I love that introduction song
@mrudulbuddhadeo7305
@mrudulbuddhadeo7305 2 жыл бұрын
I really understand the concept ....thanku sir
@soilscience6297
@soilscience6297 4 жыл бұрын
Thank you professor jave
@erenbeggarverypoor
@erenbeggarverypoor 3 жыл бұрын
I like the intro so much.and sama as professor dave
@anandswaroop1971
@anandswaroop1971 3 жыл бұрын
Thank u so much sir .....u made me understand so clearly😊😊
@timeless_escapades
@timeless_escapades 7 ай бұрын
you're a life saver 🙏🏻
@cindyle116
@cindyle116 2 жыл бұрын
thank you!! this is informative
@zjyub
@zjyub Жыл бұрын
I wish you would have shown the easier way to set up the multiplication within the vectors set up.
@masonengland306
@masonengland306 7 ай бұрын
Carrying me through calc by day. Crushing flat earther's by night
@malharshah9025
@malharshah9025 4 жыл бұрын
What is the tune during comprehension...someone plrase tell! I really like it....it is relaxing and satisfying!
@ProfessorDaveExplains
@ProfessorDaveExplains 4 жыл бұрын
it's just a dumb thing i made up! if you go to my "just for fun" playlist there is a five hour loop of it in there, just in case you fell like listening for longer!
@malharshah9025
@malharshah9025 4 жыл бұрын
Thank you professor!!!
@huyta4899
@huyta4899 Жыл бұрын
Why is it minus J on the very first step, explain please
@lufunonemakhavhani5097
@lufunonemakhavhani5097 5 жыл бұрын
tnx Mr Dave u rock 😚
@nick-no6pi
@nick-no6pi 4 жыл бұрын
thank you prof dave
@nick-no6pi
@nick-no6pi 10 ай бұрын
aint no way i came back 3 years later cos I forgot
@Aaron067
@Aaron067 Жыл бұрын
How to find the direction of the vector product of 2 vectors : 2:25 to 3:05
@mahimapatel8706
@mahimapatel8706 2 жыл бұрын
Thank you professor!
@xCharjx
@xCharjx 4 жыл бұрын
Helps a lot! Thanks Professor Dave.
@kjasalewjathan
@kjasalewjathan 2 жыл бұрын
The right hand rule remimds me of Poyntings vector
@davidmccabe6471
@davidmccabe6471 3 жыл бұрын
My University teaches us the cross product in the form i+j+k not as you have as i-j+k, do they give the same results, do you know why it's different?
@MohitBaboria
@MohitBaboria 4 ай бұрын
I think there is a misunderstanding When you expand a determinant along any row or column you will always get atleast one negative co factor
@ruirui_130
@ruirui_130 4 жыл бұрын
Thank you
@MyPiano629
@MyPiano629 4 жыл бұрын
The first one shouldn't be -3i+19j-10k?
@nanay6358
@nanay6358 4 жыл бұрын
Yes it should be -27i+19j+10k
@zainabal-dujaili2825
@zainabal-dujaili2825 4 жыл бұрын
yes you are right i find the same things
@FavourExcel-sp1jk
@FavourExcel-sp1jk 7 ай бұрын
Sir what if i am been given a number or component like a=(1,2, -3) and b=(2,-3,4) How can i solve it
@aphiwemkhwanazi2041
@aphiwemkhwanazi2041 3 жыл бұрын
the best to ever exist
@pcboom2897
@pcboom2897 3 жыл бұрын
Superb sir thank you ❤🙏
@SolidPayne
@SolidPayne 3 күн бұрын
These videos really don’t help university’s case in being a useless way of demonstrating your effectiveness in a field. 90% of the time I swear I actually get better by KZbin not lectures.
@RajKapoor-ix4mk
@RajKapoor-ix4mk 6 жыл бұрын
Hi Mr Dave.
@jaclynrosenthal6939
@jaclynrosenthal6939 3 жыл бұрын
At 2:59, the right right-hand diagram seems to show that a & b are perpendicular to each other, but they don't have to always be perpendicular, right?
@carultch
@carultch 3 жыл бұрын
True. The input vectors don't necessarily need to be perpendicular. When they are not perpendicular, the output cross product vector will still be perpendicular to both of them, and in a direction determined by the right hand rule. Simply let your middle finger rotate to a position other than perpendicular to your index finger. Your thumb will still identify the direction of the cross product resultant. The magnitude of the cross product will be the area of a parallelogram, defined by the two vectors as two of the adjacent sides of the shape. You can use this as a shortcut for finding the area of a triangle among three points in space in general. Find a vector between point A and point B, and another vector between point A and point C. Take the cross product, find its magnitude, and divide by two.
@ManyuRamKasetty
@ManyuRamKasetty Жыл бұрын
Thank you!
@AndSooOn
@AndSooOn 3 ай бұрын
Amazing. Thank you.
@pratham2636
@pratham2636 10 ай бұрын
How the +13j comes if there is a -(-5-8) equation it should be the -13
@gamexx6676
@gamexx6676 2 жыл бұрын
why did you subtract at 1:50
@ramijkhan9038
@ramijkhan9038 3 жыл бұрын
It would have been a little better if you would've shown the matrix...
@sumedhbaviskar3817
@sumedhbaviskar3817 5 жыл бұрын
bXc must be -27i -42j -16k am i right?
@adrienjoshua6710
@adrienjoshua6710 4 жыл бұрын
nope, its correct
@lunam11
@lunam11 4 жыл бұрын
It should be -43j
@haneulkim4902
@haneulkim4902 10 ай бұрын
If cross product of two vectors is orthogonal to both of them doesn't that mean new dimension is added? so if there exists two vectors in 2-d plane if we apply right hand rule does the thumb point upward introducing new 3rd dimension Z-axis?
@carultch
@carultch 8 ай бұрын
Yes. A cross product of two vectors in 2-d space, requires a third dimension for the resultant. If you cross unit vectors i-hat and j-hat, in that order, the resultant is k-hat, which produces the z-axis. By convention, a standard right-handed coordinate system, puts the x-axis (i-hat unit vector) on the pointer finger, the y-axis (j-hat unit vector) on the middle finger, and the z-axis (k-hat unit vector) on the thumb. The cross product in a purely 2-dimensional space, is just a scalar, rather than a vector. If we lived in flatland, applications of the cross product like torque, would just be scalars.
@avamcdonald4437
@avamcdonald4437 3 жыл бұрын
so helpful once again. thanks.
@khwajaabdurrehman1375
@khwajaabdurrehman1375 8 ай бұрын
Wait, in which previous video did you discuss vector dot product? I can't seem to find it in any previous video in the linear algebra series.
@ProfessorDaveExplains
@ProfessorDaveExplains 8 ай бұрын
Earlier in the big math playlist
@burningsilicon149
@burningsilicon149 6 жыл бұрын
I’m always told that the cross product is perpendicular to the 2 vectors but never given a explanation so I have to just accept as fact but Professor Dave could you please provide the reason for this.
@carultch
@carultch 3 жыл бұрын
Set up a general case of a cross product: cross |i j k| |a b c| |d e f| i*(b*f - c*e) + j*(c*d - a*f)+ k*(a*e -b*d) = Then take the dot product with the above, and the original vectors dot = a*(b*f - c*e) + b*(c*d - a*f) + c*(a*e - b*d) a*b*f - a*c*e + b*c*d - a*b*f + c*a*e - c*b*d Cancel equal and opposite terms: a*b*f - a*c*e - a*b*f + c*a*e a*b*f - a*b*f 0 Do the same with the other original vector, and you will see that the dot product of any vector and its cross product with a second vector, will always be zero. This indicates that the cross product is perpendicular to both original vectors.
@burningsilicon149
@burningsilicon149 3 жыл бұрын
@@carultch Good explanation I didn’t think of using the dot product on a general crossproduct vector to check if the resulting crossproduct vector was perpendicular to the original vectors ,but this only proof only applies to 2d crossproducts is there a more general proof that extends to general (n dimension) crossproducts.
@carultch
@carultch 3 жыл бұрын
@@burningsilicon149 The cross product proof I gave, applies to crossing two 3-dimensional vectors in general, and it shows that no matter what the vectors are, the dot product of each source vector and the cross product resultant is zero. The proof depends on it already being established that a dot product of zero means perpendicular vectors. The N-dimensional cross product doesn't really exist, as it is a concept which is only defined in 3-dimensional vector spaces. You can cross two 2-d vectors, and the result is perpendicular to the plane of both of them, requiring 3-d space to work with all three vectors. You can cross two 1-d vectors, and the result is guaranteed to be zero. But for 4-d vectors, there is no cross product defined. There are other types of vector multiplication in higher dimensional vector space, that I know nothing about.
@burningsilicon149
@burningsilicon149 3 жыл бұрын
@@carultch I wasn’t aware that above 3 dimensions the crossproduct isn’t defined.I’ve taken linear algebra and they usually extend say matrix vector multiplication to a arbitrary number of dimensions (n) I assumed that applied to crossproducts as well.
@chitochibwe1145
@chitochibwe1145 2 жыл бұрын
Why is it arranged as i-j+k
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