Proving (A X B) X C = AxBxCx (i x k) + AyBxCy (j x k) | Unit Vectors

[abrowaqas]

Homework Statement

Prove that
(A X B) X C = AxBxCx (i x k) + AyBxCy (j x k)
where i , j and k are unit vectors ?

Homework Equations

The Attempt at a Solution

let A= Axi+Ayj
B= Bxi+Byj

L.H.S = (AXB)XC
= (C.A) B - (C.B) A
= (AxCx+AyCy)(Bxi+Byj)- (BxCx+ByCy)(Axi+Ayj)
after simplification we get
= AxByCx i - AxByCy j + AyBxCy i - AyBxCx j
there i am held up... now how i proceed further..

 

[Coto]

I believe you should start by writing A and B has 3 dimensional vectors rather than 2. I would follow the exact steps you have above and then finish the problem by expanding the RHS (AxBxCx (i x k) + AyBxCy (j x k)) and showing that the two are equivalent.

 

[vela]

Homework Statement

Prove that
(A X B) X C = AxBxCx (i x k) + AyBxCy (j x k)
where i , j and k are unit vectors ?

It doesn't work for A=i, B=j, and C=i. Since B_x=0, the righthand side is equal to 0, but the lefthand side is equal to j.