AQA Further Paper 1 Specimen — Question 7 5 marks

Exam BoardAQA
ModuleFurther Paper 1 (Further Paper 1)
SessionSpecimen
Marks5
TopicVectors: Lines & Planes

7 Three planes have equations, $$\begin{gathered} x - y + k z = 3
k x - 3 y + 5 z = - 1
x - 2 y + 3 z = - 4 \end{gathered}$$ Where \(k\) is a real constant. The planes do not meet at a unique point. 7
  1. Find the possible values of \(k\) 7
  2. There are two possible geometric configurations of the given planes. Identify each possible configurations, stating the corresponding value of \(k\) Fully justify your answer.
    [0pt] [5 marks]
    7
  3. Given further that the equations of the planes form a consistent system, find the solution of the system of equations.