CAIE P1 2015 November — Question 5

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2015
SessionNovember
TopicVectors 3D & Lines

5 Relative to an origin \(O\), the position vectors of the points \(A\) and \(B\) are given by $$\overrightarrow { O A } = \left( \begin{array} { c } p - 6
2 p - 6
1 \end{array} \right) \quad \text { and } \quad \overrightarrow { O B } = \left( \begin{array} { c } 4 - 2 p
p
2 \end{array} \right)$$ where \(p\) is a constant.
  1. For the case where \(O A\) is perpendicular to \(O B\), find the value of \(p\).
  2. For the case where \(O A B\) is a straight line, find the vectors \(\overrightarrow { O A }\) and \(\overrightarrow { O B }\). Find also the length of the line \(O A\).