CAIE P1 2010 June — Question 6

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2010
SessionJune
TopicVectors: Lines & Planes

6 Relative to an origin \(O\), the position vectors of the points \(A , B\) and \(C\) are given by $$\overrightarrow { O A } = \mathbf { i } - 2 \mathbf { j } + 4 \mathbf { k } , \quad \overrightarrow { O B } = 3 \mathbf { i } + 2 \mathbf { j } + 8 \mathbf { k } , \quad \overrightarrow { O C } = - \mathbf { i } - 2 \mathbf { j } + 10 \mathbf { k }$$
  1. Use a scalar product to find angle \(A B C\).
  2. Find the perimeter of triangle \(A B C\), giving your answer correct to 2 decimal places.