Question

If A vector X B vector =B vector X A vector then find the angle between A vector and B vector if they are in different direction.

Answer 1

$Let\ \theta\ be\ angle\ from\vec{A}\ to\ \vec{B}\ in\ the\ anti-clockwise\ direction.\\Then,\ -\theta\ or\ (2\pi - \theta)\ is\ the\ angle\ from\ \vec{B}\ to\ \vec{A}\\\\given,\ \vec{A} \times \vec{B}=\vec{B} \times \vec{A}\\\\So,\ A *B*Sin\theta=B*A*\sin(2\pi - \theta)=-A*B*Sin\theta\\\\Hence,\ sin\theta=0\\\\\theta=0^0\ \ or\ \ 180^0$

The vectors A and B are aligned, either in the same direction or in the opposite directions.