CAIE P1 2012 November — Question 9

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2012
SessionNovember
TopicVectors 3D & Lines

9 The position vectors of points \(A\) and \(B\) relative to an origin \(O\) are given by $$\overrightarrow { O A } = \left( \begin{array} { c } p
1
1 \end{array} \right) \quad \text { and } \quad \overrightarrow { O B } = \left( \begin{array} { l } 4
2
p \end{array} \right)$$ where \(p\) is a constant.
  1. In the case where \(O A B\) is a straight line, state the value of \(p\) and find the unit vector in the direction of \(\overrightarrow { O A }\).
  2. In the case where \(O A\) is perpendicular to \(A B\), find the possible values of \(p\).
  3. In the case where \(p = 3\), the point \(C\) is such that \(O A B C\) is a parallelogram. Find the position vector of \(C\).