Mathematics 0580 · IGCSE · Vectors in two dimensions
Vectors in two dimensions — practice question
In the diagram shown, $O$ is the origin, $\overrightarrow{OA} = \mathbf{a}$, $\overrightarrow{OC} = \mathbf{c}$ and $\overrightarrow{AB} = \mathbf{b}$. $P$ lies on the line $AB$ such that $AP : PB = 2 : 1$. $Q$ is the midpoint of $BC$. The diagram is marked NOT TO SCALE.
(a)[1]
Find, in terms of $\mathbf{a}$, $\mathbf{b}$ and $\mathbf{c}$, the vector $\overrightarrow{CB}$.
(b)[2]
Find the position vector of $Q$, in terms of $\mathbf{a}$, $\mathbf{b}$ and $\mathbf{c}$.
(c)[2]
Find, in terms of $\mathbf{a}$, $\mathbf{b}$ and $\mathbf{c}$, the vector $\overrightarrow{PQ}$.
Worked solution & mark scheme
This 5-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Answer: $a + b - c$” …