Vector triple product expansion (very optional) | Vectors and spaces | Linear Algebra | Khan Academy

A shortcut for having to evaluate the cross product of three vectors

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[maaan]

BAC CAB rule from 'Introduction to electrodynamics' by David Griffiths - good text

[Glockd]

@sadistically
you forgot a negative for J (hat). Remember signs alter when you take the determinant of 3x3 or higher matrices. If you do the algebra again you will see that it yields the same result.

[SanrollySoccer]

sometimes an example could be really useful

[HotPepperLala]

Also, Sal, you should put this in the linear algebra/calculus playlist!

[faizanshahansari]

sub z was sounding more like hindi word "SABZI" but great work sal

[StephenRayner]

Isn't there a quicker way to do in the exam? But this is very well dome, thank you very much.

[MirahYoung]

where did the axbxcx-axbxcx come from?

[viratrantake]

Sir y component is coming negative of ((by(a.c)-cy(a.b))jcap

[MidNightRyder]

was the + axbxcx - axbxcx just to make the factoring easier? im not sure the purpose of implementing it if it doesnt do anything to the equation. But thanks!

[ujjvalpatel]

Ha ha ha, I hit like to this video you put a lot of effort to explain this simple concept..., The is for your Effort not the things explained video

[doubleja]

And yet again, something I would have never learned in school.

[rebekahshtayfman]

Around 2:05 you said, "this is just one way to remember the dot product" but I am pretty sure you meant cross product.

[Ario]

@khanacademy Khan, you have once again saved my life

[Sadistically]

Isn't the j component backwards, though?

j (axbxcy - axbycx - azbycz + azbzcy)
j (-by(axcx + azcz) + cy(axbx + azbz))

The y component of b is now negative, while the c is positive, so how does the proof still hold true?

[nirmalrajput]

Don't hire Indian teachers for Khan academy India can understand you much better . You have an explicit way to teach . Well Thank ya

[ghernandez]

Thank you so much for simplifying the math, I did not know that I had to add and subtract for the proof.

[giannisniper]

you might make a couple of video about multilinear algebra :P

[mohammadpathan]

is it correct to distribute the a ((a*b)*(a*c)) and then do a vector product (ans1 * ans2) ???

[doubleja]

@127miles
Are you a Inglish teecher?

[Crissix]

Thanks again Sal, love your videos :)