Vectors in two dimensions

$P=(3\ 4\ -5)$ and $Q=\begin{pmatrix}-1&1\\1&0\\0&-1\end{pmatrix}$.

May/June 2015

Triangle $ABC$ has vertices $A(2, 2)$, $B(3, 5)$ and $C(4, 1)$. Triangle $A'B'C'$ has vertices $A'(-4, 4)$, $B'(-3, 7)$ and $C'(-2, 3)$. Write down the column vector for the translation that takes triangle $ABC$ to triangle $A'B'C'$.

May/June 2016

The given vectors are $\vec{JK}=\begin{pmatrix}2\\5\end{pmatrix}$, $\vec{KL}=\begin{pmatrix}4\\-2\end{pmatrix}$, and $\vec{LM}=\begin{pmatrix}-1\\3\end{pmatrix}$.

May/June 2016

Vector $p$ is $\begin{pmatrix}3\\4\end{pmatrix}$, while vector $q$ is $\begin{pmatrix}-4\\3\end{pmatrix}$.

May/June 2018

The displacement vector is $\vec{AB} = \begin{pmatrix} -3 \\ 5 \end{pmatrix}$.

May/June 2021

The vectors are $\mathbf{p}=\begin{pmatrix}2\\3\end{pmatrix}$ and $\mathbf{q}=\begin{pmatrix}-3\\2\end{pmatrix}$.

May/June 2022

In quadrilateral $ABCD$, $H$, $K$, $L$ and $M$ mark the midpoints of $AB$, $BC$, $CD$ and $AD$ respectively. $\vec{AB} = 2a$, $\vec{BC} = 2b$ and $\vec{AD} = 2d$.

May/June 2024

$A$ has coordinates $(-4,5)$, while $B$ has coordinates $(6,1)$. $\vec{BC} = \begin{pmatrix}-3\\-4\end{pmatrix}$.

May/June 2025

The vector $\vec{PQ}$ has the form $\begin{pmatrix}4 \\ -2\end{pmatrix}$.

May/June 2025

The diagram displays the vectors $\vec{PQ}$ and $\vec{QR}$. $\vec{PQ} = \begin{pmatrix}5 \\ 2\end{pmatrix}$ and $\vec{QR} = \begin{pmatrix}a \\ b\end{pmatrix}$.

Oct/Nov 2015

ABCDE is a pentagon. $AFB$, $AHE$ and $BGC$ lie on straight lines.

Oct/Nov 2015

The diagram displays the points $O$ and $R$, together with the vectors $\mathbf{a}$ and $\mathbf{b}$.

Oct/Nov 2016

The diagram shows $\overrightarrow{AB} = \begin{pmatrix} -6 \\ 11 \end{pmatrix}$ and $\overrightarrow{AC} = \begin{pmatrix} 12 \\ -5 \end{pmatrix}$.

Oct/Nov 2016

Express $\begin{pmatrix}2\\1\end{pmatrix} - 3\begin{pmatrix}-1\\2\end{pmatrix} + 2\begin{pmatrix}0\\-2\end{pmatrix}$ in the form of a single vector.

Oct/Nov 2018

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

Oct/Nov 2018

The diagram displays the points $O$ and $C$, along with the vectors $\mathbf{p}$ and $\mathbf{q}$.

Oct/Nov 2019

From the diagram, $\vec{OB} = \begin{pmatrix}12\\6\end{pmatrix}$.

Oct/Nov 2019

The point $H$ has coordinates $(5, 2)$, and the point $J$ has coordinates $(-3, 6)$. Find $\vec{HJ}$.

Oct/Nov 2020

Vectors applied to coordinate geometry.

Oct/Nov 2020

The position vector of point $A$ is $\begin{pmatrix}3 \\ -7\end{pmatrix}$, and $\overrightarrow{AB}=\begin{pmatrix}-5 \\ 12\end{pmatrix}$.

Oct/Nov 2021

The position vectors for points $A$ and $B$ are provided.

Oct/Nov 2022

$ABCD$ is a parallelogram whose sides are $AB$, $BC$, $CD$ and $DA$. The point $A$ is $(-3,7)$ and the point $B$ is $(2,5)$. $\vec{AD} = \begin{pmatrix}-1\\-6\end{pmatrix}$.

Oct/Nov 2024

The figure depicts triangle OAB. $\overrightarrow{OA}=a$ and $\overrightarrow{OB}=4b$. T lies on AB so that $AT:TB=3:2$.

Oct/Nov 2025

OPQR forms a parallelogram. $\overrightarrow{OP}=a$ and $\overrightarrow{OR}=2b$. M lies halfway along QR. N is a point on PQ, with PN:NQ=1:3.

Oct/Nov 2025

Given $\mathbf{a}=\begin{pmatrix}-3\\4\end{pmatrix}$ and $\mathbf{b}=\begin{pmatrix}8\\-2\end{pmatrix}$.

Oct/Nov 2025