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N2013 P1 Q1

N2013 P1 Q1

Junior College 2
5 marks

Planes \(p\), \(q\) and \(r\) have equations \(x-2z=4\), \(2x-2y+z=6\) and \(5x-4y+\mu z=-9\) respectively, where \(\mu\) is a constant.

  1. Given that \(\mu=3\), find the coordinates of the point of intersection of \(p\), \(q\) and \(r\).[2]
  2. Given instead that \(\mu=0\), describe the relationship between \(p\), \(q\) and \(r\).[3]

Solution:

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Answer:(i) \(\left(-\frac{38}3,-\frac{119}6,-\frac{25}3\right)\). (ii) The planes intersect pairwise in three distinct parallel lines, forming the sides of a triangular prism; there is no common point.

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