If the magnitude of sum of two vectors is equal to the magnitude of difference of the two vectors, the angle between these vectors is

Solution :
Suppose two vectors are $$P$$ and $$Q.$$
It is given that $$\left| {P + Q} \right| = \left| {P - Q} \right|$$
Let angle between $$P$$ and $$Q$$ is $$\phi .$$
$$\eqalign{ & \therefore {P^2} + {Q^2} + 2PQ\cos \phi = {P^2} + {Q^2} - 2PQ\cos \phi \cr & \Rightarrow 4PQ\cos \phi = 0 \cr & \Rightarrow \cos \phi = 0\,\,\left[ {\because P,Q \ne 0} \right] \cr & \Rightarrow \phi = \frac{\pi }{2} = {90^ \circ } \cr} $$