(a)[3]
Show, using a scalar product, that angle $ABC$ is a right angle.
(b)[2]
Show that triangle $ABC$ is isosceles.
(c)[4]
Determine the exact length of the perpendicular from $O$ to the line through $B$ and $C$.
Mathematics 9709 · AS & A Level · Vectors
Vectors — practice question
Relative to the origin $O$, triangle $ABC$ has vertices with position vectors $\overrightarrow{OA} = 2i + 5k$, $\overrightarrow{OB} = 3i + 2j + 3k$ and $\overrightarrow{OC} = i + j + k$.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Express $\overrightarrow{AB}$ (or $\overrightarrow{BA}$) and $\overrightarrow{BC}$ (or $\overrightarrow{CB}$) in vector form” …
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