OCR FP3 2011 June — Question 1

Exam BoardOCR
ModuleFP3 (Further Pure Mathematics 3)
Year2011
SessionJune
TopicVectors: Lines & Planes

1 A line \(l\) has equation \(\frac { x - 1 } { 5 } = \frac { y - 6 } { 6 } = \frac { z + 3 } { - 7 }\) and a plane \(p\) has equation \(x + 2 y - z = 40\).
  1. Find the acute angle between \(l\) and \(p\).
  2. Find the perpendicular distance from the point \(( 1,6 , - 3 )\) to \(p\).