OCR MEI
Further Pure Core AS
2019
June
— Question 4
Exam Board
OCR MEI
Module
Further Pure Core AS (Further Pure Core AS)
Year
2019
Session
June
Topic
3x3 Matrices
4
Find \(\mathbf { M } ^ { - 1 }\), where \(\mathbf { M } = \left( \begin{array} { r r r } 1 & 2 & 3 - 1 & 1 & 2 - 2 & 1 & 2 \end{array} \right)\).
Hence find, in terms of the constant \(k\), the point of intersection of the planes
$$\begin{aligned}
x + 2 y + 3 z & = 19
- x + y + 2 z & = 4
- 2 x + y + 2 z & = k
\end{aligned}$$
In this question you must show detailed reasoning.
Find the acute angle between the planes \(x + 2 y + 3 z = 19\) and \(- x + y + 2 z = 4\).