OCR H240/02 2018 June — Question 2

Exam BoardOCR
ModuleH240/02 (Pure Mathematics and Statistics)
Year2018
SessionJune
TopicVectors 3D & Lines

2 The points \(A\) and \(B\) have position vectors \(\left( \begin{array} { c } 1
- 2
5 \end{array} \right)\) and \(\left( \begin{array} { c } - 3
- 1
2 \end{array} \right)\) respectively.
  1. Find the exact length of \(A B\).
  2. Find the position vector of the midpoint of \(A B\). The points \(P\) and \(Q\) have position vectors \(\left( \begin{array} { l } 1
    2
    0 \end{array} \right)\) and \(\left( \begin{array} { l } 5
    1
    3 \end{array} \right)\) respectively.
  3. Show that \(A B P Q\) is a parallelogram.