CAIE Further Paper 1 2020 November — Question 4

Exam BoardCAIE
ModuleFurther Paper 1 (Further Paper 1)
Year2020
SessionNovember
TopicVectors: Cross Product & Distances

4 The points \(A , B , C\) have position vectors $$- \mathbf { i } + \mathbf { j } + 2 \mathbf { k } , \quad - 2 \mathbf { i } - \mathbf { j } , \quad 2 \mathbf { i } + 2 \mathbf { k } ,$$ respectively, relative to the origin \(O\).
  1. Find the equation of the plane \(A B C\), giving your answer in the form \(a x + b y + c z = d\).
  2. Find the perpendicular distance from \(O\) to the plane \(A B C\).
  3. Find the acute angle between the planes \(O A B\) and \(A B C\).