If vector A x B = 0 and vector B x C = 0, then the value of vector A x C will be

Question

If \(\vec A \times \vec B = \vec 0\) and \(\vec B\times \vec C = \vec 0\), then the value of \(\vec A \times \vec C\) will be

(A) \(\vec 0\)

(B) \(AC \sin\theta \hat n\)

(C) \(AC \cos\theta \hat n\)

(D) \(-\hat n\)

Answer 1

Correct option is (A) \(\vec 0\)

\(\vec A \times \vec B = 0\)

\(AB\sin\theta = 0\)

\(\theta = 0\quad .....{(1)}\)

The angle between \(\vec A\) and \(\vec B\) is zero.

\(\vec B \times \vec C = 0\) 

\(BC\sin\phi= 0\) 

\(\phi = 0\quad .....{(2)}\) 

The angle between \(\vec B\) and \(\vec C\) is zero.

From the above discussion,

The angle between \(\vec A\) and \(\vec C\) is

\(\vec A \times \vec C = 0\)