CAIE P3 2016 November — Question 10

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2016
SessionNovember
TopicVectors: Lines & Planes

10 The line \(l\) has vector equation \(\mathbf { r } = \mathbf { i } + 2 \mathbf { j } + \mathbf { k } + \lambda ( 2 \mathbf { i } - \mathbf { j } + \mathbf { k } )\).
  1. Find the position vectors of the two points on the line whose distance from the origin is \(\sqrt { } ( 10 )\).
  2. The plane \(p\) has equation \(a x + y + z = 5\), where \(a\) is a constant. The acute angle between the line \(l\) and the plane \(p\) is equal to \(\sin ^ { - 1 } \left( \frac { 2 } { 3 } \right)\). Find the possible values of \(a\).