(a)[5]
Determine a vector equation for the line passing through $M$ and $N$.
(b)[3]
The line through $M$ and $N$ meets the line through $O$ and $B$ at $P$. Find the position vector of $P$.
(c)[3]
Calculate angle $OPM$, giving the answer in degrees.
Mathematics 9709 · AS & A Level · Vectors
Vectors — practice question
Using $O$ as the origin, the position vectors of $A$ and $B$ are $
\overrightarrow{OA} = 6\mathbf{i} + 2\mathbf{j}$ and $\overrightarrow{OB} = 2\mathbf{i} + 2\mathbf{j} + 3\mathbf{k}$. $M$ is the midpoint of $OA$. Point $N$, which lies on $AB$ between $A$ and $B$, satisfies $AN = 2NB$.