Motion of a particle in a plane is described by the non-orthogonal set of coordinates $$(p, q)$$ with unit vectors $$(\hat{p}, \hat{q})$$ inclined at an angle $$\theta$$ as shown in the diagram. If the mass of the particle is $$m$$, its kinetic energy is given by $$\left(\dot{x} = \frac{dx}{dt}\right)$$

A

$$\frac{1}{2} m\left(\dot{p}^2 + \dot{q}^2 + \dot{p}\dot{q}\cos\theta\right)$$

B

$$\frac{1}{2} m\left(\dot{p}^2 + \dot{q}^2 - \dot{p}\dot{q}(1 - \sin\theta)\right)$$

C

$$\frac{1}{2} m\left(\dot{p}^2 + \dot{q}^2 + 2\dot{p}\dot{q}\cos\theta\right)$$

D

$$\frac{1}{2} m\left(\dot{p}^2 + \dot{q}^2 + \dot{p}\dot{q}\cot\theta\right)$$