OCR C4 — Question 8

Exam BoardOCR
ModuleC4 (Core Mathematics 4)
TopicVectors 3D & Lines

8. The points \(A\) and \(B\) have coordinates \(( 3,9 , - 7 )\) and \(( 13 , - 6 , - 2 )\) respectively.
  1. Find, in vector form, an equation for the line \(l\) which passes through \(A\) and \(B\).
  2. Show that the point \(C\) with coordinates \(( 9,0 , - 4 )\) lies on \(l\). The point \(D\) is the point on \(l\) closest to the origin, \(O\).
  3. Find the coordinates of \(D\).
  4. Find the area of triangle \(O A B\) to 3 significant figures.