Question

Given that vector P+Q=P-Q this will be true only when___________

Answer 1

Answer:

Given, P+Q=P−Q

Comparing the square of magnitudes, we have

P2+Q2+2PQcosθ=P2+Q2−2PQcosθ

Thus, either cosθ=0 or one of the two vectors is a null vector. If P is null, then P+Q=P−Q gives Q=−Q, implying both are null, which is absurd.

Also if they are perpendicular, the direction of sum and difference of vectors will be different, so that case is also ruled out. Hence it can happen only if Q is null vector.