Question 6 • Exam Practice
7 Marks
The line L has equation \mathbf{r} = \begin{pmatrix} 1 \\ -2 \\ 3 \end{pmatrix} + \lambda \begin{pmatrix} 2 \\ 1 \\ -1 \end{pmatrix} . The plane \Pi has Cartesian equation 3x - 2y + 4z = 13 . (a) Find the coordinates of the point where L intersects \Pi . [4 marks] (b) Determine whether L is perpendicular to \Pi . Justify your answer. [3 marks]
Answer: (a) \ \text{No point of intersection (the line is parallel to the plane)}, \quad (b) \ \text{Not perpendicular as } \mathbf{b} \neq k\mathbf{n}