(a)[5]
Find the position vectors of the two points on the line whose distance from the origin is $\sqrt{10}$.
(b)[5]
The plane $p$ is given by $ax + y + z = 5$, where $a$ is a constant. The acute angle between the line $l$ and the plane $p$ is $\sin^{-1}\!\left( \dfrac{2}{3} \right)$. Find the possible values of $a$.