9709 P31 - Nov 2023 - Q11 - 10 marks
2231
In the cuboid \(OABCDEFG\), \(OA=3,\ OC=2,\ OD=2\). Unit vectors \(\mathbf i,\mathbf j,\mathbf k\) are parallel to \(OA,OD,OC\), respectively. \(M\) is the midpoint of \(EF\).
(a) Find the position vector of \(M\). [1]
The position vector of \(P\) is \(\mathbf i+\mathbf j+2\mathbf k\).
(b) Calculate angle \(PAM\). [4]
(c) Find the exact length of the perpendicular from \(P\) to the line through \(O,M\). [5]
