Prove the following: a) If $ABCA'B'C'$ is a right prism and $M \in (BC), N \in (CA), P \in (AB)$ such that $A'M, B'N$ and $C'P$ are perpendicular each other and concurrent, then the prism $ABCA'B'C'$ is regular. b) If $ABCA'B'C'$ is a regular prism and $\frac{AA'}{AB}=\frac{\sqrt6}{4}$ , then there are $M \in (BC), N \in (CA), P \in (AB)$ so that the lines $A'M, B'N$ and $C'P$ are perpendicular each other and concurrent.