CAIE P1 2011 November — Question 3

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2011
SessionNovember
TopicVectors 3D & Lines

3 Relative to an origin \(O\), the position vectors of points \(A\) and \(B\) are given by $$\overrightarrow { O A } = 5 \mathbf { i } + \mathbf { j } + 2 \mathbf { k } \quad \text { and } \quad \overrightarrow { O B } = 2 \mathbf { i } + 7 \mathbf { j } + p \mathbf { k }$$ where \(p\) is a constant.
  1. Find the value of \(p\) for which angle \(A O B\) is \(90 ^ { \circ }\).
  2. In the case where \(p = 4\), find the vector which has magnitude 28 and is in the same direction as \(\overrightarrow { A B }\).