CAIE P3 2002 June — Question 8

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2002
SessionJune
TopicVectors: Lines & Planes

8 The straight line \(l\) passes through the points \(A\) and \(B\) whose position vectors are \(\mathbf { i } + \mathbf { k }\) and \(4 \mathbf { i } - \mathbf { j } + 3 \mathbf { k }\) respectively. The plane \(p\) has equation \(x + 3 y - 2 z = 3\).
  1. Given that \(l\) intersects \(p\), find the position vector of the point of intersection.
  2. Find the equation of the plane which contains \(l\) and is perpendicular to \(p\), giving your answer in the form \(a x + b y + c z = 1\).