A rectangular coil of dimensions $5\mathrm{.}40cm8\mathrm{.}50cm$ lies in the $x-y$ plane and consists of $25$ turns of wire. The current in each loop is $15\mathrm{.}0$ mA clockwise, and an external magnetic field given by $B=(0\mathrm{.}7i+0\mathrm{.}5j-0\mathrm{.}8k)$ Tesla magnetic field is applied to the coil.

a$)$ Calculate the magnetic dipole moment of the coil and give its direction using unit vector notation. $(7$ Points$)$

b$)$ Calculate the magnitude of the torque acting on the coil. $(7$ Points$)$

c$)$ the potential energy $U,$ stored in the coil. $(6$ Points$)$