Vectors Practice Questions

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

Write $\vec{QR}$ as a column vector.

Write $\vec{RP}$ as a column vector.

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

Work out $\mathbf{b} - \mathbf{a}$ as a column vector.

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

Work out $\mathbf{p} + 2\mathbf{q}$ as a column vector.

Here are three more vectors.

$\mathbf{r} = \begin{pmatrix}10\\-4\end{pmatrix}$ $\mathbf{s} = \begin{pmatrix}-5\\-2\end{pmatrix}$ $\mathbf{t} = \begin{pmatrix}2\\-5\end{pmatrix}$

Write down which one of these vectors is parallel to $\mathbf{p}$.
Give a reason for your answer.

$\mathbf{a} = \begin{pmatrix}1\\-2\end{pmatrix}$ and $\mathbf{b} = \begin{pmatrix}2\\3\end{pmatrix}$

On the grid, draw the vector $\mathbf{a} + 2\mathbf{b}$.
Label the vector.

Write $\vec{OQ}$ in terms of $\mathbf{a}$.

Write $\vec{PS}$ in terms of $\mathbf{a}$ and $\mathbf{b}$.

Write $\vec{OU}$ in terms of $\mathbf{a}$ and $\mathbf{b}$.

Write $\vec{AB}$ in terms of $\mathbf{a}$ and $\mathbf{b}$.

Write $\vec{MN}$ in terms of $\mathbf{a}$ and $\mathbf{b}$.
Give your answer in its simplest form.

Salma says that $MN$ is parallel to $AB$.

Is Salma correct? You must give a reason for your answer.