Mathematics 0580 · IGCSE · Vector geometry

Vector geometry — practice question

In the diagram, $\overrightarrow{OA} = a$ and $\overrightarrow{OB} = b$. The ratio $AK : KB = 2 : 1$. Also, $OK = KC$. The diagram is marked "NOT TO SCALE".
(main)[4]

Find $\overrightarrow{AC}$ in terms of $a$ and $b$. Present your answer in the simplest form.

Worked solution & mark scheme

This 4-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Working: $\vec{AK}=\dfrac{2}{3}(-a+b)$” …

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