Help with the vector triple product

A

alain

du hast mich
Registered Senior Member
Hey, sorry to bug you all, but I would like some help proving the vector triple product

ie that

U x (V x W) = (U.W)V - (U.V)W

If anyone could help me out that would be awesome.

Thanks
 
(a×b)×c = (c·a)b - (b·c)a

Proof:

Let a = [a1,a2,a3], and let b and c be defined similarly.

a×b = [a2b3-a3b2, a3b1-a1b3, a1b2-a2b1]

(a×b)×c = [(a3b1-a1b3)c3-(a1b2-a2b1)c2, (a1b2-a2b1)c1-(a2b3-a3b2)c3, (a2b3-a3b2)c2-(a3b1-a1b3)c1]
(a×b)×c = [a3b1c3-a1b3c3-a1b2c2+a2b1c2, a1b2c1-a2b1c1-a2b3c3+a3b2c3, a2b3c2-a3b2c2-a3b1c1+a1b3c1]

This is equal to (c·a)b - (b·c)a, which you can verify using the same method as in the Lagrange formula, above.
 
Lagrange's formula makes me want to dream of everlasting fall into nothingness but real illusions of the never to come tomorrow that I so much love.
 
OK, sorry once again. I'm having some difficulty expanding
(c.a)b - (b.c)a
would you be able to help me out their too

thanks
 
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