Help with the vector triple product

Discussion in 'Physics & Math' started by alain, Mar 31, 2007.

1. alaindu hast michRegistered Senior Member

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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

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5. draqonBannedBanned

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(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.

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7. draqonBannedBanned

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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.

8. alaindu hast michRegistered Senior Member

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Thanks so much

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9. alaindu hast michRegistered Senior Member

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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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ask absane.