Vector Algebra

Statement I : Two forces $\left( {\overrightarrow P + \overrightarrow Q } \right)$ and $\left( {\overrightarrow P - \overrightarrow Q } \right)$ where $\overrightarrow P \bot \overrightarrow Q$, when act at an angle $\theta$₁ to each other, the magnitude of their resultant is $\sqrt {3({P^2} + {Q^2})}$, when they act at an angle $\theta$₂, the magnitude of their resultant becomes $\sqrt {2({P^2} + {Q^2})}$. This is possible only when ${\theta _1} < {\theta _2}$. Statement II : In the situation given above. $\theta$₁ = 60$^\circ$ and $\theta$₂ = 90$^\circ$ In the light of the above statements, choose the most appropriate answer from the options given below :-