Calculus 3 Lecture 11.3: Using the Dot Product

Calculus 3 Lecture 11.3: Using the Dot Product: Explanation of the Dot Product, Finding the angle between two vectors including how the Dot Production show orthogonal vectors, Vector Projection, Work, and Direction angles.

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[MrTickleMePinkFloyd]

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[ProfessorLeonard]

Hi everybody!! Please remember, Youtube takes AWHILE before it pushes out Full1080p60pHD. Just wanted to get it out ASAP for you all. Enjoy!

[jayanoris]

Note to self:

Ex: 7:58 Simple dot product

Ex: 20:40 Dot product + addition

Ex: 28:40 Adding magnitudes

Ex: 1:05:10 Finding angle between two vectors

Ex: 1:11:30 Are two vectors parallel or perpendicular?

Ex: 1:42:35 Vector projections

Ex: 2:00:20 Find work

Ex: 2:06:10 Find work given angles

Ex: 2:24:05 Direction cosines

Ex: 2:26:23 Find cos alpha, beta, gamma

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[grey]

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[Peter_]

My trick for memorizing the whole "projection" notation at 1:43:20 is to think of the fact that the subscript, _which is typically written as a _*_small_*_ letter, _ represents the projection vector, _which is generally _*_smaller_*_ than the projected vector._
So basically, the small subscript letter represents the smaller projection vector.

Of course, it is true that the actual vector *"a"* in this video is originally a potentially larger vector, but I am talking about the part of the vector *a* that actually becomes the projection of vector *b.*

You can of course also think of the word "subscript" as a reminder that that vector is "below" the original projected vector, as long as you stick to the convention that the projected vector is drawn above the projection vector.

[Xenaprez]

the way that my jaw literally dropped when you showed us WHY the dot product of two vectors being zero means they are orthogonal!!!! thank you for showing every step of logic and for helping us understand it fully

[danielisenberg]

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[paradox]

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[JohnnyBoun]

omg! six years ago??!! yeah. Prof. Soupman, ich du liebe, man.... I just got my proper workstation set up after a few years of cp struggles. now, after all that, I am ready, quite ready, to learn dot products!!! Then.... wait for it.... wait for it.... CROSS PRODUCT!!.
Thanks beyond reason, my fave soup(er) professor Mr. Leo the lion. - rd. JB.

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