AQA Further Paper 1 Specimen — Question 9 10 marks

Exam BoardAQA
ModuleFurther Paper 1 (Further Paper 1)
SessionSpecimen
Marks10
TopicVectors: Lines & Planes

9 A line has Cartesian equations \(x - p = \frac { y + 2 } { q } = 3 - z\) and a plane has
equation r. \(\left[ \begin{array} { r } 1
- 1
- 2 \end{array} \right] = - 3\) 9
  1. In the case where the plane fully contains the line, find the values of \(p\) and \(q\).
    [0pt] [3 marks]
    9
  2. In the case where the line intersects the plane at a single point, find the range of values of \(p\) and \(q\).
    [0pt] [3 marks]
    9
  3. In the case where the angle \(\theta\) between the line and the plane satisfies \(\sin \theta = \frac { 1 } { \sqrt { 6 } }\) and the line intersects the plane at \(z = 0\) 9
    1. Find the value of \(q\).
      [0pt] [4 marks]
      9
  4. (ii) Find the value of \(p\).