Answer
See the detailed answer below.
Work Step by Step
$$\color{blue}{\bf [a]}$$
Recalling that
$$\vec F=q\vec v\times \vec B $$
So according to the right-hand rule for a negative charge, which is opposite the direction determined by the right-hand rule for a positive charge, the magnetic field $\vec B$ must be $45^\circ$ counterclockwise from positive $x$-axis on the same plane of $\vec v$
$$\color{blue}{\bf [b]}$$
By the same approach, using the right-hand rule, the magnetic field $\vec B$ must be $45^\circ$ clockwise from positive $x$-axis on the same plane of $\vec F$
