When a particle of charge $q >$ 0 moves with a velocity of $\vec{v}$$1$ 1 at 45.0$^\circ$ from the $+x$-axis in the $xy$-plane, a uniform magnetic field exerts a force $\overrightarrow{F}_1$ along the $-z$-axis ($\textbf{Fig. P27.51}$). When the same particle moves with a velocity $\overrightarrow{v}_2$ with the same magnitude as $\overrightarrow{v}_2$ 1 but along the $+z$-axis, a force $\overrightarrow{F}_2$ of magnitude $F_2$ is exerted on it along the $+x$-axis. (a) What are the magnitude (in terms of $q$, $v_1$, and $F_2$) and direction of the magnetic field? (b) What is the magnitude of $\overrightarrow{F}_1$ in terms of $F2$ ?