OCR Further Pure Core 2 2022 June — Question 10

Exam BoardOCR
ModuleFurther Pure Core 2 (Further Pure Core 2)
Year2022
SessionJune
TopicVectors: Lines & Planes

10 The coordinates of the points \(A\) and \(B\) are ( \(3 , - 2 , - 1\) ) and ( \(13,10,9\) ) respectively.
  • The plane \(\Pi _ { A }\) contains \(A\) and the plane \(\Pi _ { B }\) contains \(B\).
  • The planes \(\Pi _ { A }\) and \(\Pi _ { B }\) are parallel.
  • The \(x\) and \(y\) components of any normal to plane \(\Pi _ { A }\) are equal.
  • The shortest distance between \(\Pi _ { A }\) and \(\Pi _ { B }\) is 2 .
There are two possible solution planes for \(\Pi _ { A }\) which satisfy the above conditions.
Determine the acute angle between these two possible solution planes.