Vectors Practice Questions

Write $\overrightarrow{AB}$ as a column vector.

$C$ is the point such that $\overrightarrow{BC}=\begin{pmatrix}-4\\-2\end{pmatrix}$.

Write down the coordinates of $C$.

Work out the length of $\overrightarrow{AB}$.

Give your answer correct to 1 decimal place.

Write $\mathbf{u}$ as a column vector.

Work out $2\mathbf{u}+\mathbf{v}$ as a column vector.

On the grid, draw and label the vector $\mathbf{u}-\mathbf{v}$.

Express $\overrightarrow{PR}$ in terms of $\mathbf{a}$ and $\mathbf{b}$.

Express $\overrightarrow{PS}$ in terms of $\mathbf{a}$ and $\mathbf{b}$.

Give your answer in its simplest form.

Write $\overrightarrow{PQ}$ as a column vector.

Work out the exact length of $PQ$.

Give your answer in the form $k\sqrt{5}$, where $k$ is an integer.

$N$ is the point on the line $PQ$ such that $PN:NQ=3:1$.

Find the position vector of $N$.

Work out $2\mathbf{a}+5\mathbf{b}$ as a column vector.

The vector $\mathbf{c}=\begin{pmatrix}8\\k\end{pmatrix}$, where $k$ is a positive number.

The magnitude of $\mathbf{c}$ is $17$.

Find the value of $k$.

Express $\overrightarrow{PQ}$ in terms of $\mathbf{a}$ and/or $\mathbf{b}$.

Give your answer in its simplest form.

Prove that $PQRS$ is a parallelogram.

Express $\overrightarrow{CD}$ in terms of $\mathbf{a}$ and $\mathbf{c}$.

Give your answer in its simplest form.

Prove that $C$, $E$ and $D$ lie on the same straight line.

Write down the ratio $CE:ED$.

$OPQ$ is a triangle.

$\overrightarrow{OP}=\mathbf{p}$ and $\overrightarrow{OQ}=\mathbf{q}$.

$R$ is the point on $PQ$ such that $PR:RQ=1:2$.

$S$ is the point on $OQ$ such that $OS:SQ=1:3$.

$T$ is the point on $OR$ such that $\overrightarrow{OT}=k\,\overrightarrow{OR}$, where $k$ is a scalar.

$PTS$ is a straight line.

Find the value of $k$.

Express $\overrightarrow{AC}$ in terms of $\mathbf{a}$ and $\mathbf{d}$.

Show that $AX:XC=1:3$.

You must show all your working.