Working out angle between vectors?

Question

I don't know how to approach this question:

Given that p=2i+j and q=i-3j, find, in degrees to 1 decimal plaec, the angle made with the vector i by the vector p

Answer 1

Hint

Use the dot (or 'scalar') product; with $\theta$ the angle between $\mathbf{p}$ and $\mathbf{q}$, one has: $$\mathbf{p} \cdot \mathbf{q} = \left\|\mathbf{p}\right\|\left\|\mathbf{q}\right\|\cos\theta \iff \cos\theta = \ldots$$

Answer 2

You can do this by using that $|p\cdot q|=|p||q|\cdot\cos(\alpha)$; and where $p=\binom21$ and $q=\binom{1}{-3}$.

This results in $|p\cdot q|=1$ and $|p||q|=\sqrt{5\cdot 10}$, so $\cos\alpha=1/\sqrt{50}$ or $\alpha\approx81.9^\circ$.