OCR Further Pure Core 1 2021 November — Question 4

Exam BoardOCR
ModuleFurther Pure Core 1 (Further Pure Core 1)
Year2021
SessionNovember
TopicVectors: Cross Product & Distances

4 Points \(A , B\) and \(C\) have coordinates ( \(4,2,0\) ), ( \(1,5,3\) ) and ( \(1,4 , - 2\) ) respectively. The line \(l\) passes through \(A\) and \(B\).
  1. Find a cartesian equation for \(l\).
    \(M\) is the point on \(l\) that is closest to \(C\).
  2. Find the coordinates of \(M\).
  3. Find the exact area of the triangle \(A B C\).