OCR MEI Further Pure Core AS 2023 June — Question 8

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

8 The equations of three planes are $$\begin{array} { r } 2 x + y + 3 z = 3
3 x - y - 2 z = 2
- 4 x + 3 y + 7 z = k \end{array}$$ where \(k\) is a constant.
  1. By considering a suitable determinant, show that the planes do not meet at a single point.
  2. Given that the planes form a sheaf, determine the value of \(k\).