Mathematics 9709 · AS & A Level · Coordinate geometry
Coordinate geometry — practice question
Relative to the origin $O$, the position vectors of points $A$ and $B$ are $\vec{OA} = \begin{pmatrix} 6 \\ -2 \\ -6 \end{pmatrix}$ and $\vec{OB} = \begin{pmatrix} 3 \\ k \\ -3 \end{pmatrix}$, with $k$ a constant.
(i)[2]
Find the value of $k$ that gives $\angle AOB = 90^\circ$.
(ii)[2]
Find the values of $k$ for which $OA$ and $OB$ are equal in length.
(iii)[4]
Point $C$ is defined by $\vec{AC} = 2\vec{CB}$. When $k = 4$, find the unit vector in the direction of $\vec{OC}$.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme.