Mathematics 4024 · O Level · Vector geometry

Vector geometry — practice question

$OAB$ forms a triangle. $P$ is on $AB$ and $AP : PB = 2:3$. $\overrightarrow{OA} = 4a$ and $\overrightarrow{OP} = 3a + 2b$.

(a(i))[1]

Find $\overrightarrow{AP}$, in terms of $a$ and $b$, and give your answer in its simplest form.

(a(ii))[3]

Find the vector $\overrightarrow{OB}$.

(b)[1]

$Q$ is placed on $OA$ so that $\overrightarrow{QP}$ runs parallel to $\overrightarrow{OB}$. Find $\overrightarrow{QP}$.

Worked solution & mark scheme

This 5-mark question has a full step-by-step worked solution and mark scheme. One marking point: “$-a+2b$” …