N2007 P1 Q6

Referred to the origin \(O\), the position vectors of the points \(A\) and \(B\) are \(\mathbf i-\mathbf j+2\mathbf k\) and \(2\mathbf i+4\mathbf j+\mathbf k\) respectively.

1. Show that \(OA\) is perpendicular to \(OB\).[2]
2. Find the position vector of the point \(M\) on the line segment \(AB\) such that \(AM:MB=1:2\).[3]
3. The point \(C\) has position vector \(-4\mathbf i+2\mathbf j+2\mathbf k\). Use a vector product to find the exact area of triangle \(OAC\).[4]