CAIE P1 2011 November — Question 6

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2011
SessionNovember
TopicVectors: Lines & Planes

6 Relative to an origin \(O\), the position vectors of points \(A\) and \(B\) are \(3 \mathbf { i } + 4 \mathbf { j } - \mathbf { k }\) and \(5 \mathbf { i } - 2 \mathbf { j } - 3 \mathbf { k }\) respectively.
  1. Use a scalar product to find angle \(B O A\). The point \(C\) is the mid-point of \(A B\). The point \(D\) is such that \(\overrightarrow { O D } = 2 \overrightarrow { O B }\).
  2. Find \(\overrightarrow { D C }\).