CAIE P3 2017 November — Question 10

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2017
SessionNovember
TopicVectors: Lines & Planes

10 Two planes \(p\) and \(q\) have equations \(x + y + 3 z = 8\) and \(2 x - 2 y + z = 3\) respectively.
  1. Calculate the acute angle between the planes \(p\) and \(q\).
  2. The point \(A\) on the line of intersection of \(p\) and \(q\) has \(y\)-coordinate equal to 2 . Find the equation of the plane which contains the point \(A\) and is perpendicular to both the planes \(p\) and \(q\). Give your answer in the form \(a x + b y + c z = d\).