Help with the vector triple product

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

 

Log in or Sign up to hide all adverts.

http://mathworld.wolfram.com/VectorTripleProduct.html

 

Log in or Sign up to hide all adverts.

(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.

 

Log in or Sign up to hide all adverts.

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.

 

Thanks so much

Please Register or Log in to view the hidden image!

 

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

 

ask absane.