Calculate the magnitude of the vector.

Here are the solutions to your questions:

a) Find the magnitude and bearing of the vector $\vec{OQ} = \begin{pmatrix} 4 \\ -6 \end{pmatrix}$.

Step 1: Calculate the magnitude of the vector.
The magnitude of a vector $\begin{pmatrix} x \\ y \end{pmatrix}$ is given by $\sqrt{x^2 + y^2}$.

$$|\vec{OQ}| = \sqrt{4^2 + (-6)^2}$$ $$|\vec{OQ}| = \sqrt{16 + 36}$$ $$|\vec{OQ}| = \sqrt{52}$$ $$|\vec{OQ}| \approx 7.211$$

Step