OCR MEI Further Pure Core 2023 June — Question 14

Exam BoardOCR MEI
ModuleFurther Pure Core (Further Pure Core)
Year2023
SessionJune
Topic3x3 Matrices

14 Three planes have equations $$\begin{aligned} k x - z & = 2
- x + k y + 2 z & = 1
2 k x + 2 y + 3 z & = 0 \end{aligned}$$ where \(k\) is a constant.
  1. By considering a suitable determinant, show that the three planes meet at a point for all values of \(k\).
  2. Using a matrix method, find, in terms of \(k\), the coordinates of the point of intersection of the planes.