OCR MEI Further Pure Core AS 2020 November — Question 9

Exam BoardOCR MEI
ModuleFurther Pure Core AS (Further Pure Core AS)
Year2020
SessionNovember
Topic3x3 Matrices

9 Three planes have equations
\(k x + y - 2 z = 0\)
\(2 x + 3 y - 6 z = - 5\)
\(3 x - 2 y + 5 z = 1\)
where \(k\) is a constant. Investigate the arrangement of the planes for each of the following cases. If in either case the planes meet at a unique point, find the coordinates of that point.
  1. \(k = - 1\)
  2. \(k = \frac { 2 } { 3 }\)