Mathematics 4024 · O Level · Vector geometry

Vector geometry — practice question

$OAC$ forms a triangle, and $B$ lies on $AC$ with $AB : BC = 3 : 2$. $\overrightarrow{OA} = \vec{a}$ and $\overrightarrow{OB} = \vec{b}$.

(a)[3]

Express $\overrightarrow{OC}$ using $\vec{a}$ and $\vec{b}$, and give the answer in its simplest form.

(b)[2]

Point $D$ lies on $OC$ and satisfies $\overrightarrow{OD} = \vec{b} - \frac{2}{5}\vec{a}$. Show that $OABD$ is a trapezium.

Worked solution & mark scheme

This 5-mark question has a full step-by-step worked solution and mark scheme. One marking point: “$\frac{5}{3}b-\frac{2}{3}a$” …