CAIE P1 2010 June — Question 5

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2010
SessionJune
TopicVectors 3D & Lines

5 Relative to an origin \(O\), the position vectors of the points \(A\) and \(B\) are given by $$\overrightarrow { O A } = \left( \begin{array} { r } - 2
3
1 \end{array} \right) \quad \text { and } \quad \overrightarrow { O B } = \left( \begin{array} { l } 4
1
p \end{array} \right)$$
  1. Find the value of \(p\) for which \(\overrightarrow { O A }\) is perpendicular to \(\overrightarrow { O B }\).
  2. Find the values of \(p\) for which the magnitude of \(\overrightarrow { A B }\) is 7 .