2007 H2 Mathematics

Paper 1 Question 6

Referred to the origin $O,$ the position vectors of the points $A$ and $B$ are

$𝐢 - 𝐣 + 2 𝐤 and 2 𝐢 + 4 𝐣 + 𝐤$

respectively.

(a)

Show that the $O A$ is perpendicular to $O B .$

[2]

(b)

Find the position vector of the point $M$ on the line segment $A B$ such that $A M : M B = 1 : 2 .$

[3]

(c)

The position vector $C$ has position vector $- 4 𝐢 + 2 𝐣 + 2 𝐤 .$ Use a vector product to find the exact area of triangle $O A C .$

[4]