Vectors Proof Questions

Hard28%

$PQRSTU\,$ is a regular hexagon with centre $O$ .

\vec{OP} = \mathbf{p}

\vec{OQ} = \mathbf{q}

$M\,$ is a point on $QR\,$ such that $QM : M R = 2 : 1$ . $X\,$ is the point on $PQ\,$ extended, such that $P Q : QX = 1 : 1$ .

Prove that $T$ , $M\,$ and $X\,$ are on the same straight line.

[5]

Vectors Proof Questions Questions