Moderate -0.3 This is a standard textbook exercise on line intersection requiring systematic equation setup and solving a 3×2 system. While it involves multiple steps (equating components, solving for parameters, verification), the method is routine and well-practiced. Slightly easier than average because it's guaranteed to intersect (no need to handle the non-intersection case) and the arithmetic is manageable.
9 Two straight lines have equations
$$\mathbf { r } = \left( \begin{array} { r }
16 \\
2 \\
3
\end{array} \right) + \lambda \left( \begin{array} { r }
3 \\
2 \\
- 1
\end{array} \right) \quad \text { and } \quad \mathbf { r } = \left( \begin{array} { r }
- 3 \\
8 \\
12
\end{array} \right) + \mu \left( \begin{array} { r }
5 \\
- 6 \\
- 3
\end{array} \right) .$$
Show that the two lines intersect and find the coordinates of their point of intersection.