OCR C4 2008 June — Question 4

Exam BoardOCR
ModuleC4 (Core Mathematics 4)
Year2008
SessionJune
TopicVectors 3D & Lines

4 Relative to an origin \(O\), the points \(A\) and \(B\) have position vectors \(3 \mathbf { i } + 2 \mathbf { j } + 3 \mathbf { k }\) and \(\mathbf { i } + 3 \mathbf { j } + 4 \mathbf { k }\) respectively.
  1. Find a vector equation of the line passing through \(A\) and \(B\).
  2. Find the position vector of the point \(P\) on \(A B\) such that \(O P\) is perpendicular to \(A B\).