(a)[4]
Show that $OA=OB$ and use a scalar product to determine angle $AOB$ in degrees.
(b)[6]
Let $M$ be the midpoint of $AB$. A point $P$ on the line through $O$ and $M$ satisfies $PA : OA = \sqrt{7} : 1$. Find the possible position vectors of $P$.
Mathematics 9709 · AS & A Level · Vectors
Vectors — practice question
Relative to origin $O$, the position vectors of points $A$ and $B$ are $\overrightarrow{OA} = 2\mathbf{i} - \mathbf{j}$ and $\overrightarrow{OB} = \mathbf{j} - 2\mathbf{k}$.