Question

Prove that (A × B)2 + (A · B)2 = A2B2

A and B are vectors.

Answer 1

(AXB)^2 + (A.B)^2=A^2 B^2--->eq 1
But
AXB=AB Sin theta (Magnitude)
A.B=AB Cos theta put in eq 1

(AB Sin theta)^2 + (AB Cos theta)^2= A^2 B^2
A^2 B^2(Sin^2 theta+ Cos^2 theta)=A^2 B^2 ... But Sin^2 theta+Cos^2=1

A^2 B^2(1)=A^2 B^2
A^2 B^2=A^2 B^2 Hence proved.