CAIE P1 2015 June — Question 9

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2015
SessionJune
TopicVectors: Lines & Planes

9 Relative to an origin \(O\), the position vectors of points \(A\) and \(B\) are given by $$\overrightarrow { O A } = 2 \mathbf { i } + 4 \mathbf { j } + 4 \mathbf { k } \quad \text { and } \quad \overrightarrow { O B } = 3 \mathbf { i } + \mathbf { j } + 4 \mathbf { k }$$
  1. Use a vector method to find angle \(A O B\). The point \(C\) is such that \(\overrightarrow { A B } = \overrightarrow { B C }\).
  2. Find the unit vector in the direction of \(\overrightarrow { O C }\).
  3. Show that triangle \(O A C\) is isosceles.