CAIE P3 2007 June — Question 9

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2007
SessionJune
TopicVectors: Lines & Planes

9
\includegraphics[max width=\textwidth, alt={}, center]{8580dddb-cc72-4745-9e0f-1ac641c6506d-3_693_537_1206_804} The diagram shows a set of rectangular axes \(O x , O y\) and \(O z\), and three points \(A , B\) and \(C\) with position vectors \(\overrightarrow { O A } = \left( \begin{array} { l } 2
0
0 \end{array} \right) , \overrightarrow { O B } = \left( \begin{array} { l } 1
2
0 \end{array} \right)\) and \(\overrightarrow { O C } = \left( \begin{array} { l } 1
1
2 \end{array} \right)\).
  1. Find the equation of the plane \(A B C\), giving your answer in the form \(a x + b y + c z = d\).
  2. Calculate the acute angle between the planes \(A B C\) and \(O A B\).