AQA C4 2012 January — Question 8

Exam BoardAQA
ModuleC4 (Core Mathematics 4)
Year2012
SessionJanuary
TopicVectors 3D & Lines

8 The points \(A\) and \(B\) have coordinates \(( 4 , - 2,3 )\) and \(( 2,0 , - 1 )\) respectively. The line \(l\) passes through \(A\) and has equation \(\mathbf { r } = \left[ \begin{array} { r } 4
- 2
3 \end{array} \right] + \lambda \left[ \begin{array} { r } 1
5
- 2 \end{array} \right]\).
    1. Find the vector \(\overrightarrow { A B }\).
    2. Find the acute angle between \(A B\) and the line \(l\), giving your answer to the nearest degree.
  1. The point \(C\) lies on the line \(l\) such that the angle \(A B C\) is a right angle. Given that \(A B C D\) is a rectangle, find the coordinates of the point \(D\).