AQA C4 2007 January — Question 6

Exam BoardAQA
ModuleC4 (Core Mathematics 4)
Year2007
SessionJanuary
TopicVectors 3D & Lines

6 The points \(A , B\) and \(C\) have coordinates \(( 3 , - 2,4 ) , ( 5,4,0 )\) and \(( 11,6 , - 4 )\) respectively.
    1. Find the vector \(\overrightarrow { B A }\).
    2. Show that the size of angle \(A B C\) is \(\cos ^ { - 1 } \left( - \frac { 5 } { 7 } \right)\).
  1. The line \(l\) has equation \(\mathbf { r } = \left[ \begin{array} { r } 8
    - 3
    2 \end{array} \right] + \lambda \left[ \begin{array} { r } 1
    3
    - 2 \end{array} \right]\).
    1. Verify that \(C\) lies on \(l\).
    2. Show that \(A B\) is parallel to \(l\).
  2. The quadrilateral \(A B C D\) is a parallelogram. Find the coordinates of \(D\).