OCR FP3 2013 June — Question 6

Exam BoardOCR
ModuleFP3 (Further Pure Mathematics 3)
Year2013
SessionJune
TopicVectors: Lines & Planes

6 The plane \(\Pi\) has equation \(x + 2 y - 2 z = 5\). The line \(l\) has equation \(\frac { x - 1 } { 2 } = \frac { y + 1 } { 5 } = \frac { z - 2 } { 1 }\).
  1. Find the coordinates of the point of intersection of \(l\) with the plane \(\Pi\).
  2. Calculate the acute angle between \(l\) and \(\Pi\).
  3. Find the coordinates of the two points on the line \(l\) such that the distance of each point from the plane \(\Pi\) is 2 .