(a) (i) A rectangular loop of sides a and b carrying current $I$ is placed in a magnetic field $\vec{B}$ such that its area vector $\vec{A}$ makes an angle $\theta$ with $\vec{B}$. With the help of a suitable diagram, show that the torque $\vec{\tau}$ acting on the loop is given by $\vec{\tau} = \vec{m} \times \vec{B}$, where $\vec{m} \ (= I\vec{A})$ is the magnetic dipole moment of the loop.