Mathematics 0580 · IGCSE · Vectors in two dimensions

Vectors in two dimensions — practice question

The vectors are $\mathbf{a}=\begin{pmatrix}-3\\8\end{pmatrix}$ and $\mathbf{b}=\begin{pmatrix}2\\-5\end{pmatrix}$.
(a(i)(a))[1]

the vector $\mathbf{b}-\mathbf{a}$

(a(i)(b))[2]

the vector $2\mathbf{a}+\mathbf{b}$

(a(i)(c))[2]

$|\mathbf{b}|$

(a(ii))[3]

Find the value of $k$ and the value of $m$.

(b(i))[1]

Express, in terms of $\mathbf{p}$ and $\mathbf{q}$, and in simplest form, $\overrightarrow{OB}$.

(b(i)(b))[2]

Find the vector $\overrightarrow{CM}$.

(b(i)(c))[2]

Find the vector $\overrightarrow{MN}$.

(b(ii))[3]

Find the position vector of $D$ in terms of $\mathbf{p}$ and $\mathbf{q}$, and give the answer in simplest form.

Worked solution & mark scheme

This 16-mark question has a full step-by-step worked solution and mark scheme. One marking point: the resulting vector $\begin{pmatrix}5\\-13\end{pmatrix}$

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