Question

prove that |A vector × B vector| + (A vector . B vector) = A^2B^2.

Answer 1

yeHere ×× is a cross product.

(A→+B→)×(A→−B→)(A→+B→)×(A→−B→)

=(A→×A→+B→×A→−A→×B→−B→×B→(A→×A→+B→×A→−A→×B→−B→×B→

Now A→×A→=0→A→×A→=0→ and B→×B→=0→B→×B→=0→ and A→×B→=−B→×A→A→×B→=−B→×A→

so we get (A→+B→)×(A→−B→)(A→+B→)×(A→−B→) =B→×A→−A→×B→B→×A→−A→×B→=2(B→×A→)2(B→×A→)