OCR FP3 2012 January — Question 4

Exam BoardOCR
ModuleFP3 (Further Pure Mathematics 3)
Year2012
SessionJanuary
TopicVectors: Cross Product & Distances

4 The line \(l\) has equations \(\frac { x - 1 } { 2 } = \frac { y - 1 } { 3 } = \frac { z + 1 } { 2 }\) and the point \(A\) is ( \(7,3,7\) ). \(M\) is the point where the perpendicular from \(A\) meets \(l\).
  1. Find, in either order, the coordinates of \(M\) and the perpendicular distance from \(A\) to \(l\).
  2. Find the coordinates of the point \(B\) on \(A M\) such that \(\overrightarrow { A B } = 3 \overrightarrow { B M }\).