How to do Vectors with triangles?

Question

This is my homework and I have just started learning it and I don't really quite understand it.

Answer 1

Hints: \begin{align*} \vec{BC} = \vec{BD} + \vec{DC} = \vec{BD} + \frac{1}{3}\vec{BD} = \cdots \\ \vec{BA} + \vec{AD} = \vec{BD} \iff \textbf{p} + \vec{AD} = \textbf q \iff \cdots \\ \vec{BC} + \vec{CA} = \vec{BA} \iff \cdots \end{align*}