OCR MEI Further Pure Core 2024 June — Question 11

Exam BoardOCR MEI
ModuleFurther Pure Core (Further Pure Core)
Year2024
SessionJune
TopicVectors: Cross Product & Distances

11 The plane \(\Pi\) has equation \(2 x - y + 2 z = 4\). The point \(P\) has coordinates \(( 8,4,5 )\).
  1. Calculate the shortest distance from P to \(\Pi\). The line \(L\) has equation \(\frac { x - 2 } { 3 } = \frac { y } { 2 } = \frac { z + 3 } { 4 }\).
  2. Verify that P lies on L .
  3. Find the coordinates of the point of intersection of L and \(\Pi\).
  4. Determine the acute angle between L and \(\Pi\).
  5. Use the results of parts (b), (c) and (d) to verify your answer to part (a).