Scalar triple prosuct

Question

 Suppose that u•(vxw) = 3 , find u•( wxv)  . Please give everyone a detailed explanation on how to solve !

Answer 1

For 2 vectors, v and w,  in R³, the cross product, v x w, is "anticommutative".  That is, v x w = -(w x v).

 

So, if u•(v x w) = 3, then u•(w x v) = u•[-(v x w)] = -[u•(v x w)] = -3.   

Answer 2

Commutative property allows the multiplication to be done in any order

 

u*(vxw) = u*(vwx) = u*(wvx) = u*(wxv)