OCR MEI Further Pure Core 2024 June — Question 15

Exam BoardOCR MEI
ModuleFurther Pure Core (Further Pure Core)
Year2024
SessionJune
TopicIntegration using inverse trig and hyperbolic functions

15 Three planes have equations $$\begin{aligned} x + k y + 3 z & = 1
3 x + 4 y + 2 z & = 3
x + 3 y - z & = - k \end{aligned}$$ where \(k\) is a constant.
  1. Show that the planes meet at a point except for one value of \(k\), which should be determined.
  2. Show that, when the planes do meet at a point, the \(y\)-coordinate of this point is independent of \(k\).