Calculus, Vectors, Projection of a Vector onto another Vector

[BlindHurricane5]

all i wanted was an explanation of the formula!

[ihsankayili]

@BlindHurricane5

Formula for the vector projection of vector U onto vector V:

(Dot product of U and V) / (magnitude of vector V) squared x vector V

[dimebagplan]

This example is very easy to understand. thank you very much.

I like how you used the shadow as an example. It make it really easy to visualize and understand.

[ihsankayili]

@dimebagplan Thank you very much.

[ramezsayed]

Great video sir it's really simple and useful........ thanks

[ihsankayili]

@ramezsayed Thank you very much.

[silverflame92]

Jazaakallah brother!

the third point 65/35 could've been reduced to 13/7 right?

[ihsankayili]

@silverflame92 It is right. Thanks...

[24BrianRulez24]

Is there some order of operations saying the dot product comes before multiplication? Otherwise I don't see why projection of u onto v is not the vector u itself. And if there is, how could we tell whether it's the dot product and it's not just multiplication by a vector.

[ihsankayili]

@24BrianRulez24 Sorry for my late respond, I did not quite understand your question. Can you please clarify?

[24BrianRulez24]

@ihsankayili I was wondering why we can't cancel out vector V times Vector V (which is equal to magnitude of V squared) with the term in the denominator. Thus get vector u times 1 which gives us vector u. It seems though as if we can't change the order and multiply vector V first with vector V and then multiply by vector u....I don't know if this is some property of the dot product

[ihsankayili]

@24BrianRulez24 You cannot cancel out v here: (u.v/v.v)v

You can cancel like this:

Numerator of the projection formula: u.v = |u|.|v|.cos A

Denominator of the projection formula: v.v = |v|.|v|.cos 90 = |v|.|v|

Result after canceling: (|u|. cos A/|v|)v. it is more complicated to calculate.

Ihsan

[o1sin182]

Great video, the analogy of projections as shadows helped me to finally wrap my head around projections. Thanks so much

[ihsankayili]

@o1sin182 Thank you.

[BrounWright]

Great video! You make this very simple to understand! I'll definitely be back over the summer to check out some of your other videos.

[ihsankayili]

@BrounWright Thanks you very much.

[BrounWright]

@ihsankayili I should have also said thank you. Pardon me please.  Many thanks - I got two questions right on my Statics final yesterday because of your video!!

[ihsankayili]

@BrounWright Thanks, congratulations.

[aulen300]

this video is pretty good comparing to others, good stuff.

[ihsankayili]

@aulen300 Thank you,

[ImanOcean100]

I am actually crying because I finally understand it, thanks you so much! :D

[ihsankayili]

@ImanOcean100 Thank you very much.

[BrounWright]

@ImanOcean100 That's beautiful.  Now I'm crying because you cried!

[Atsuke]

Thanks so much! You explained what a projection is and all it took was just 1 minute for me to understand while my professor at UCLA took the whole lecture and we still walked out confused.

[ihsankayili]

@Atsuke Thank you.

[ihsankayili]

@KNooboob Thank you.

[yxooo]

BIG thank You. Wish you were our math teacher

[ihsankayili]

@yxooo Thank you.

[JPraise100]

AWESOME!!!!!!!!!!! JOB

[ihsankayili]

@JPraise100 Thanks

[TheDaftSmiley]

Excellent video! Thanks for the explanation.

[ihsankayili]

@TheDaftSmiley Thank you.

[Reggae4Triceratops]

thanks bro.

[ihsankayili]

@Reggae4Triceratops Thank you.

[ihsankayili]

@davidallany1 Thank you, tesekkurler.

[asalad083]

Mr. ihsankayili, you are amazing instructor, your camera was clear and your explanation of the problem was brilliant. I also liked the multiple ways that you were solving the problem and got the same answer. thank you very much for your time,

[ihsankayili]

@asalad083

Hi, Thanks for your kind comment.

Ihsan



[robman85]

Wonderful explanation. Thank you!

[ihsankayili]

@robman85

Thanks for your comment. Ihsan

[Avinator100]

what happens if U is longer than v ????

[ihsankayili]

@Avinator100

You follow the same method even if u is longer than v. You can reduce the size of v. Example: v = (1/2 , 3/2 , 5/2). The result does not change.

[TheBucksB]

Thanks a lot. Really helps.

[ihsankayili]

@TheBucksB Thanks for your comment.  Ihsan

[MetallicAus]

thanks. your the man

[yellow4452]

Thank you for the clear and simple explanation, in less than 10 minutes I could understand more than in 3 lectures.

[ihsankayili]

Thank you for your comment.

[ihsankayili]

@yellow4452

Thank you very much.

[TheHammy713]

Oh my god!! This makes sense now! Thank you so much for posting this video!

[ihsankayili]

Thanks you for your commment.

[xxxcoolboyxxx]

You have very nice way of explaining things. Thank you very much!

[ihsankayili]

Thank you.

[krynble]

Hello, Ihsan, I just used your teaching on a computer graphics program I'm designing. Just writing to thank you for your great job. Omar Ajoue, from Brazil.

[ihsankayili]

Thank you krynble.

[GraemeB1967]

The video is good because you start with the theory and know what you are talking about. It is better if you do not repeat what you have already written and stay on the task showing the process. After you have completed then you can comment about how parallel vectors will come up with the same result. The problem in explainng it before is it is harder to follow.

Please do more as your knowledge on the subject is more than most who do videos.

[ihsankayili]

Hi, Thanks for your comment. I appreciate it. I will consider your critics in my future videos. Thanks again. Ihsan

[ihsankayili]

Thank you very much

[MaverickCentricity]

Amazing work. Much Appreciated.

[ihsankayili]

Thanks

[SikWidIt007]

amazing .