Question

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Answer 1

Vector A + Vector B = Vector A - Vector B

Taking Modulus both sides,

| Vector A + Vector B | = | Vector A -

Vector B |

$\sqrt{{A} ^{2} + {B} ^{2} + \:2\: A. B\: cos \:theta}$ = $\sqrt{{A} ^{2} + {B} ^{2}\: - \:2\: A. B\: cos \:theta}$

2 A. B cos theta = - 2 A. B cos theta

4 A. B cos theta = 0

Cos theta = 0°

Theta = 90°

Hence, the Vector A and Vector B are non - zero vectors and are perpendicular to each other.

So, OPTION ( 1 ). is correct.

( a ). Vector A. Vector B = 0