The linear velocity of a rotating body is given by $\overrightarrow v = \overrightarrow \omega \times \overrightarrow r,$ where $\overrightarrow \omega$ is the angular velocity and $\overrightarrow r$ is the radius vector. If the angular velocity of a body is $\overrightarrow \omega = \hat i - 2\hat j + 2\hat k$ and the radius vector is $\overrightarrow r = 4\hat j - 3\hat k,$ then find the magnitude of linear velocity $|\overrightarrow v |$.

• A
  $\sqrt {29} \text{ units}$
• B
  $\sqrt {31} \text{ units}$
• C
  $\sqrt {37} \text{ units}$
• D
  $\sqrt {41} \text{ units}$