Calculus 3 - Vector Projections & Orthogonal Components

This calculus 3 video tutorial explains how to find the vector projection of u onto v using the dot product and how to find the vector component of u orthogonal to v. W1 is the component of u parallel to v and w2 is the component of u perpendicular to v.
3D Coordinate System:
• Plotting Points In a T...
3D Distance Formula:
• How To Find The Distan...
Equation of a 3D Sphere:
• How To Find The Equati...
Calculus 3 - Intro to Vectors:
• Calculus 3 - Intro To ...
Calculus 3 - The Dot Product:
• Calculus 3 - The Dot P...
_______________________________
Angle Between Two Vectors:
• Finding The Angle Betw...
Parallel & Orthogonal Vectors:
• Are The Two Vectors Pa...
Direction Cosines and Vectors:
• Calculus 3 - Direction...
Calculus 3 - Vector Projections:
• Calculus 3 - Vector Pr...
Cross Product of 2 Vectors:
• Cross Product of Two V...
_______________________________
Area - Vector Cross Product:
• Area of a Parallelogra...
Triple Scalar Product:
• Volume of a Parallelep...
Vector Equations of Lines:
• How To Find The Vector...
The Equation of a Plane:
• How To Find The Equati...
Planar Equation - 3 Points:
• How To Find The Equati...
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[@TheOrganicChemistryTutor]

Final Exams and Video Playlists: www.video-tutor.net/

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I was so confused after my lesson in college, but now I actually understand vector projections. tysm you have the best explanations

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[@georgesadler7830]

Professor Organic Chemistry Tutor, thank you for another excellent video/lecture on Vector Projections and Orthogonal Components in Calculus Three. Vector Projections and Orthogonal Components are also used in Engineering Electromagnetics and Engineering Physics. This is an error free video/lecture on KZbin TV with the Organic Chemistry Tutor.

[@mangore623]

Perfectly explained. Short and sweet, with none of the usual BS.

[@fordon20s]

Also a way to check would be to verify that either “W2” dot V =0. That just proves again that they are perpendicular to each other. 1st example, W2 dot V = (2/5*10/5+(-1/5)*20/5)=0 any other answer means there is an error somewhere.

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[@DengMamStenkt]

Great video! Instead of dividing by the squared magnitude of v, you can also divide by v dot v, which is a bit quicker.

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[@ian.ambrose]

2:25 Isn't W2 supposed to be component of vector U that is orthogonal to vector V instead?

[@liamh02]

Yes

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[@reamabdulsalam524]

Hi can you please post a tutorials supporting us with vector projection into a line ? And if you have two vectors how do we produce 3 time 3 orthogonal projection matrix which projects on to sub space donned by these vectors

[@cubby091398]

I got an A in Calculus II but that has been over 15 years ago. I wonder if it would be ok to take Calculus III since I know what your saying about vectors and I know how to do some basic multiple integration.

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[@derekwang7330]

Can anyone explain how he got the formula at 3:45?

[@beastIsI2001]

Please could you do linearly dependent and linearly independent vectors

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[@MagnusTheGreat]

Just remembering how to do this for Calc 3 final lol

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[@archirnobenz]

I would prefer if you explained the reason the formula 4:35 was used rather than just giving me the formula and to use it. Like the definition of that formula, what does that formula mean? Like why is it divided by the square of v?

[@faustoestrella2272]

more calc 3 videos please

[@malakasadalikhan109]

2:45 Example1 (2D) 3:55/7:43(4:35), , 5:47Ans(w1) 6:12 7:05Ans(w2) Example2 (3D) 7:15

[@rollicconducto1550]

Did you say the correct definition of W2 at 2:20? The one that you mentioned does not look like orthogonal to me

[@damiandark48]

Might not be the best place to say this but, could someone link me to a video about projections which we use to find the shortest distance between two 3d vectors?

[@medwards764]

2:24 Error? Shouldn't it be that w2 is the component of vector u that is orthogonal to vector v?

[@jachinchyn3845]

that's what I thought too

[@badreddinegacem]

Ikr

[@alex-my8hp]

2:19 you got u and v the wrong way round. Still, great video.

[@3stepsahead704]

I was wondering about the dame,thank you for confirming

[@Sequence1994]

was searching for this - thanks

[@khloud_m]

Please anyone tell me what the program name he use it to make this video

[@IAmNumber4000]

Bruh the textbook wrote this stuff in the most incomprehensible way possible. The notation they use takes about 10x to read and understand as the way you’ve written it.

[@nugusujemal2317]

Please do vidio on n spaces

[@devangshikarmakar4646]

Awesome

[@abeimnida]

Is this the gram schmidt orthogonalizatiob?

[@user-xq3jq3cf2f]

The formula for prpjector is different it should be (u×v/||u||^2 ) u

[@joseph_walter3957]

i Write the decomposition v = w − q of vector v into the orthogonal components w and q, where w is the projection of v onto u and q is a vector orthogonal to the direction of u. PLEASE HOW DO YOU UNDERSTAND THIS QUESTION ABOVE AND CAN YOU PLEASE EXPLAIN TO ME

[@culturevulture2850]

Beast

[@Dora-rs4mc]

Comment je montre que le produit de deux vecteur de ⃗a∧⃗b est orthogonale à chacun des deux vecteurs ⃗a et ⃗b

[@noonespecial3536]

But where does the formula for the projection come from?

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[@chrischoir3594]

what is the name of that formula?

[@Hammadmk971]

Can someone please explain to me why at @02:47 - w2 is said to equal "u-w1"? Thanks in advance!

[@alexanimates13]

He’s basically saying that vector u without w1 (which is the x axis of the vector) is just a vertical line aka w2 He just broke down vector u into the x(w1) and 6(w2) components is all its saying

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i love you

[@NOVAsteamed]

4:15 what is the origin of that formula? Anyone has the proof?

[@bismahsadaqat4129]

i suggest you learn really flawlessly about unit vectors