An electron is moving with a velocity $\vec{v} = (2 \hat{i} + 3 \hat{j}) \text{ m/s}$ in an electric field $\vec{E} = (3 \hat{i} + 6 \hat{j} + 2 \hat{k}) \text{ V/m}$ and a magnetic field $\vec{B} = (2 \hat{j} + 3 \hat{k}) \text{ T}$. Calculate the magnitude and direction (with $x$-axis) of the Lorentz force acting on the electron.

• A
  $9.6 \times 10^{-19} \text{ N}, \theta = \cos^{-1}\left(\frac{2}{\sqrt{5}}\right)$
• B
  $9.6 \times 10^{-19} \text{ N}, \theta = \cos^{-1}\left(\frac{5}{\sqrt{2}}\right)$
• C
  $2.15 \times 10^{-18} \text{ N}, \theta = \cos^{-1}\left(\frac{2}{\sqrt{5}}\right)$
• D
  $2.15 \times 10^{-18} \text{ N}, \theta = \cos^{-1}\left(\frac{5}{3}\right)$