Mathematics 4024 · O Level · Vectors in two dimensions

Vectors in two dimensions — practice question

For point A, the position vector $\vec{OA}$ is $\begin{pmatrix}-4 \\ 7\end{pmatrix}$, and $\vec{AB} = \begin{pmatrix}6 \\ -3\end{pmatrix}$.

(a)[1]

Find the position vector $\vec{OB}$ for point $B$.

(b)[2]

Find the magnitude $|\vec{AB}|$.

(c)[2]

Find the coordinates of point $C$, given that $\vec{AB} = 3\vec{CB}$.

(d(i))[3]

Since line $L$ is parallel to $AB$ and goes through the point $(-2,5)$, find the equation of line $L$.

(d(ii))[1]

Line $M$ is perpendicular to line $L$ and passes through the origin. Find the equation of line $M$.

Worked solution & mark scheme

This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Answer: $\begin{pmatrix}2\\4\end{pmatrix}$” …