The resultant of vectors $${\vec P}$$ and $${\vec Q}$$ is $${\vec R}.$$ On reversing the direction of $${\vec Q},$$ the resultant vector becomes $${\vec S}.$$ Then, correct relation is

Solution :
We have $${R^2} = {P^2} + {Q^2} + 2PQ\cos \theta \,......\left( {\text{i}} \right)$$
$${\text{and}}\,\,{S^2} = {P^2} + {Q^2} - 2PQ\cos \theta \,......\left( {{\text{ii}}} \right)$$
Adding equations (i) and (ii), we get
$${R^2} + {S^2} = 2\left( {{P^2} + {Q^2}} \right).$$