Cross product introduction | Vectors and spaces | Linear Algebra | Khan Academy

Introduction to the cross product

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[driesforce]

And for all this time I was thinking math teachers couldn't draw for shit. This guy comes along and draws a near perfect hand.

[MrChewwy]

Just here to show some love for that sweet hand.

[hathbeenslain]

That hand drawing really woke me up. I was paying attention and noting things down but I wasn't really into it until that beautiful drawing. Thanks, Sal! Who says math teachers can't draw!

[siddharthaganguly]

"assuming that you're anatomically similar to me" that line cracked me up XD

[annlee]

Hand drawing pretty good
And surprised to find comments r all about the hand haha

[thereidmcgowan]

Holy shit that thumb thing was a game-changer

[tjentertainmentstudio]

Sal, you are HILARIOUS and it's interesting to see how you teach as you literally explain EVERY step of the way not only to the audience, but to yourself too as you do it to confirm your own knowledge. Just brilliant dude.

[FahimusAlimus]

Hands are almost universally the hardest body part to draw for artists but you just pulled that off effortlessly, can we have some art tutorials as well as maths ones?

[Hasheesh]

this guys is a fucking boss. not only can he do math, but he can draw

[anandib]

Today I came to know that SAL is not only a good math teacher & mathematician, he is also good at drawing.

[civicsproject]

As a college engineering freshman, this stuff is gold!!!! Thanks!

[Excalibaard]

I think the crossproduct is easier to remember if you draw the a vectors underneath again. for the second element, you do a3 times the b1 you drew underneath the original b3, - a1 that you drew under a3, times b3. that makes it easier to remember without 'doing opposites and such', you just expand your box. for the third, basically you do the cross of the elements underneath again, which is again a1b2 - a2b1.

[whocaresifyouexist]

The satisfaction of cancelling out till 0 is just something i cant explain.

[DlcEnergy]

almost everyone here is commenting just for the hand. i'm just over here really glad you proved the cross product dot a or b cancel out back to 0. i never thought to prove that in the definition. it makes much more sense knowing that.

but btw, nice bloody hand drawing.

[birogrenci]

Khan Academy, Could you translate cross product and dot product to Turkish please?🙏

[shambhunathmandal]

I got my answer which I was searching for so many days thanks a lot.

[lukas]

Where would i be without Sal! Great hand btw.

[mikelord]

There's an easier way to do it: instead of taking the terms all confusing together x=(x1, x2, x3) y=(y1, y2, y3) you can make a matrix with z=(i, j, k) of the form
| i, j , k |
det |x1, x2, x3| = i(x2*y3 - x3*y2)+j(x3*y1 -
|y1, y2, y3| x1*y3)+k(x1*y2 - x2*y1)
and you have your terms

[shiroxyui]

Anime drawing style right there. I know you are a fan of anime. >.> Khan. Let us exchange some words and drink tea. 

[tharunragumar]

another mindhint for memorizing think of
[a1, a2, a3] then exclude then from the equation so first row don't have a1 [a2b3-a3b2]vertically the order of first terms 231