(i)[2]
Prove that $\overrightarrow{CP} = 2.4\mathbf{i} - 1.8\mathbf{k}$.
(ii)[2]
Write $\overrightarrow{OP}$ and $\overrightarrow{BP}$ using $\mathbf{i}$, $\mathbf{j}$ and $\mathbf{k}$.
(iii)[4]
Use the scalar product to determine angle $BPC$.
Mathematics 9709 · AS & A Level · Coordinate geometry
Coordinate geometry — practice question
The diagram depicts a pyramid $OABC$ with a flat triangular base $OAB$ and perpendicular height $OC$. Angles $AOB$, $BOC$ and $AOC$ are each right angles. Unit vectors $\mathbf{i}$, $\mathbf{j}$ and $\mathbf{k}$ run parallel to $OA$, $OB$ and $OC$ respectively, and $OA = 4$ units, $OB = 2.4$ units and $OC = 3$ units. Point $P$ lies on $CA$ so that $CP = 3$ units.