Interpret parametric lines and zero cross products

(a) Interpret geometrically the vector equation $\mathbf r=\mathbf a+t\mathbf b$, where $\mathbf a$ and $\mathbf b$ are constant vectors and $t$ is a parameter.

(b) The points $P$, $Q$ and $R$ have position vectors $\mathbf p$, $\mathbf q$ and $\mathbf r$ respectively. The points $P$ and $Q$ are fixed and $R$ varies. Given that $\mathbf p$ is non-zero and $(\mathbf r-\mathbf p)\times\mathbf q=\mathbf0$, describe geometrically the set of all possible positions of the point $R$.