Problem

The plane $\Pi_1$ contains the point $A(2,4,-5)$ and is normal to the vector

$$\begin{pmatrix} 1\\ 3\\ 3 \end{pmatrix}$$

The plane $\Pi_2$ contains the point $B(3,6,-2)$ and is normal to the vector

$$\begin{pmatrix} 2\\ 0\\ -5 \end{pmatrix}$$

The line $l$ is the line of intersection of $\Pi_1$ and $\Pi_2$

(a) Determine a vector equation for $l$.

The points $C$ and $D$ both lie on $l$.

Given that $C$ and $D$ are 5 units apart,

(b) determine the exact volume of the tetrahedron $ABCD$.