CAIE P1 2017 June — Question 8

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2017
SessionJune
TopicVectors 3D & Lines

8 Relative to an origin \(O\), the position vectors of three points \(A , B\) and \(C\) are given by $$\overrightarrow { O A } = 3 \mathbf { i } + p \mathbf { j } - 2 p \mathbf { k } , \quad \overrightarrow { O B } = 6 \mathbf { i } + ( p + 4 ) \mathbf { j } + 3 \mathbf { k } \quad \text { and } \quad \overrightarrow { O C } = ( p - 1 ) \mathbf { i } + 2 \mathbf { j } + q \mathbf { k }$$ where \(p\) and \(q\) are constants.
  1. In the case where \(p = 2\), use a scalar product to find angle \(A O B\).
  2. In the case where \(\overrightarrow { A B }\) is parallel to \(\overrightarrow { O C }\), find the values of \(p\) and \(q\).