Question 41
Let $VABC$ be a regular tetrahedron of side length $a$ and points $M$, $N$ on the edges $VB$, $VC$, such that $VM = \frac{a}{3}$ and $VN = \frac{a}{6}$. If $Q$ is the projection of $V$ onto the plane $(AMN)$ and $O$ is the projection of $V$ onto the plane $(ABC)$, compute the lengths of the segments $VO$, $VQ$, and a trigonometric function of the angle between the straight lines $VQ$ and $VO$.