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  4. A x B = B x A, then the angle between A and B is

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Q. A x B = B x A, then the angle between A and B is

BHUBHU 2003Motion in a Plane

Solution:

(A x B)=(B x A)
$\Rightarrow (A \times B) - (B \times A) = 0 \, \, \, \, \, \, [\because (B \times A) = - (A \times B)]$
(A x B) + (A x B) = 0
$\Rightarrow 2 (A \times B) = 0 \, \Rightarrow \, \, \, 2ABsin \, \theta = 0$
$ sin \, \theta = 0$
$\because [|A| = A \ne 0; \, \, |B| = B \ne 0]$
$\therefore \theta = 0 \, \, or \, \, \pi$