CAIE P3 2019 June — Question 10

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2019
SessionJune
TopicVectors: Cross Product & Distances

10 The line \(l\) has equation \(\mathbf { r } = \mathbf { i } + 2 \mathbf { j } + 3 \mathbf { k } + \mu ( 2 \mathbf { i } - \mathbf { j } - 2 \mathbf { k } )\).
  1. The point \(P\) has position vector \(4 \mathbf { i } + 2 \mathbf { j } - 3 \mathbf { k }\). Find the length of the perpendicular from \(P\) to \(l\).
  2. It is given that \(l\) lies in the plane with equation \(a x + b y + 2 z = 13\), where \(a\) and \(b\) are constants. Find the values of \(a\) and \(b\).
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