Answer
The magnetic field is directed horizontally at an angle of $56.4^{\circ}$ north of west or $56.4^{\circ}$ south of east.
Work Step by Step
We can find the angle $\theta$ between the velocity vector and the magnetic field:
$F = q~v ~B~sin~\theta$
$sin~\theta = \frac{F}{q~v~B}$
$\theta = arcsin~(\frac{F}{q~v~B})$
$\theta = arcsin~\left(\frac{3.2 \times 10^{-14}~N}{(-1.6\times 10^{-19}~C)(2.0\times 10^5~m/s)(1.2~T)}~\right)$
$\theta = 56.4^{\circ}$
Since the charge of the electron is negative, by the right hand rule, the magnetic field must be directed horizontally at an angle of $56.4^{\circ}$ north of west or $56.4^{\circ}$ south of east.
