Question

Assuming U, V and W are vectors. Prove that (u×v)•((v×w)×(w×u))=(u•(v×w))^2

Hints: Use a×(b×c)=b(a•c)-c(a•b) and a•(b×c)=b•(c×a)=c•(a×b)

Answer 1

the function as per first formula can be re written as \[u \times v ( w((v \times w). u - u ((v \times w ) . w)\]
\[v \times w \] is perpendicular to w and hence their dot product is 0
the remaining terms by second formula becomes the RHS