If θ be the angle between vector A and vector B, then the magnitude of (vector B x vector A ). vector A

Question

If θ be the angle between \(\vec A\) and \(\vec B\), then the magnitude of \((\vec B\times\vec A).\vec A\) will be:

(a) BA² cos θ

(b) BA² sin θ

(c) BA² sin θ.cos θ

(d) Zero

Answer 1

Correct option is : (d) Zero

\(\vec B\times\vec A = B.A.\sin\theta.\hat{i} = \vec R\)

The direction of \(\vec R\) will be at right angles to plane of \(\vec A\) and \(\vec B\).

\(i.e\ \vec R\bot\vec A\)

Hence, \((\vec B\times\vec A).\vec A = \vec R.\vec A\) = R.A. cos 90° = 0 (zero)

Thus, alternative (d) is correct.