Question

Prove (A×B) ×( C ×D) = [A ∙ (C ×D)]B − [B ∙( C ×D ] A

Answer 1

you work out the LHS first

Answer 2

then the RHS

Answer 3

and it is correct if
LHS=RHS

Answer 4

ill work it out for you if you explain to me what the dot is

Answer 5

oh it's a dot product A ∙B = AxBx +AyBy + AzBz

Answer 6

but do you understand how to prove now

Answer 7

i know how to prove i just don't know how to expand the LHS to make it look like in the RHS. Our professor said we are only allowed to expand the LHS. :)

Answer 8

@martaamador62
i have responded on physics forum

Answer 9

you need to understand how the vector triple product works and also how you can fiddle about very freely with the signs and vector orders in the trip scalar prod.

and, yes, you only need to play with the LHS to solve this.

Answer 10

thank you :)

Answer 11

nice problem

Answer 12

I think this is the Jacobi Identity of cross product while treating \(\mathbf{C}\times\mathbf{D}\) as a single vector.