Mathematics 4024 · O Level · Vector geometry

Vector geometry — practice question

In the parallelogram $OABC$, $\overrightarrow{OA} = 2a$ and $\overrightarrow{OC} = 3c$. $M$ is the midpoint of $BC$, and $T$ lies on $OB$ with $OT : TB = 2 : 1$.
(a)[1]

Find $\overrightarrow{OB}$, giving your answer in terms of $a$ and $c$.

(b(i))[1]

Express, in terms of $a$ and $c$ and in its simplest form, $\overrightarrow{AM}$.

(b(ii))[2]

Express, in terms of $a$ and $c$ and as simply as possible, $\overrightarrow{AT}$.

(c)[2]

Show that $ATM$ lies on a straight line.

Worked solution & mark scheme

This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: “$2a + 3c$” …

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