Mathematics 0580 · IGCSE · Vectors in two dimensions

Vectors in two dimensions — practice question

OABC is a parallelogram with O at the origin. $CK = 2KB$ and $AL = LB$. $M$ is the midpoint of $KL$. $\overrightarrow{OA} = \mathbf{p}$ and $\overrightarrow{OC} = \mathbf{q}$. The diagram has been drawn NOT TO SCALE.
(a)[2]

Find, in terms of $\mathbf{p}$ and $\mathbf{q}$, and give your answer in simplest form, $\overrightarrow{KL}$.

(b)[2]

Determine the position vector of $M$.

Worked solution & mark scheme

This 4-mark question has a full step-by-step worked solution and mark scheme. One marking point: Simplified result: $\frac{1}{3}p-\frac{1}{2}q$

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