Mathematics 0580 · IGCSE · Vectors in two dimensions
Vectors in two dimensions — practice question
The diagram indicates that $OAB$ is a triangle, while $ABC$ and $PQC$ are straight lines. $P$ is the midpoint of $OA$, $Q$ is the midpoint of $PC$, and $OQ : QB = 3 : 1$. Also, $\vec{OA} = 4a$ and $\vec{OB} = 8b$. NOT DRAWN TO SCALE.
(a(i))[1]
Find, in terms of $a$ and/or $b$, and in its simplest form, $\vec{AB}$.
(a(ii))[1]
Find, in terms of $a$ and/or $b$, and in its simplest form, $\vec{OQ}$.
(a(iii))[1]
Find, in terms of $a$ and/or $b$, and in its simplest form, $\vec{PQ}$.
(b)[3]
Using vectors, find the ratio $AB : BC$.
Worked solution & mark scheme
This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: “The simplified result is $8b-4a$.” …