\( \newcommand\mycolv[1]{\begin{pmatrix}#1\end{pmatrix}} \)
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Vector Connectors

Exercises about vectors and coordinates

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This is level 3: find the column vector given the negative vector or larger coordinates. You will be awarded a trophy if you get at least 9 correct and you do this activity online.


The point \(O\) is the origin.
The point \(B\) is \((-29, -25)\).

Find the position vector \(\overrightarrow{OB}\)


The point \(O\) is the origin.
The point \(D\) is \((-8, 5)\).

Find the position vector \(\overrightarrow{OD}\)


The point \(O\) is the origin.
The point \(F\) is \((0, 27)\).

Find the position vector \(\overrightarrow{OF}\)


The vector \(\overrightarrow{GH}\) is\( \mycolv{-5\\-9} \)

Find the vector \(\overrightarrow{HG}\).


The vector \(\overrightarrow{IJ}\) is\( \mycolv{-4\\-5} \)

Find the vector \(\overrightarrow{JI}\).


The vector \(\overrightarrow{KL}\) is\( \mycolv{-3\\2} \)

Find the vector \(\overrightarrow{LK}\).


The point \(M\) is \((22, -28)\).
The point \(N\) is \((19, -27)\).

Find the column vector \(\overrightarrow{MN}\)


The point \(O\) is \((-5, 26)\).
The point \(P\) is \((19, -6)\).

Find the column vector \(\overrightarrow{OP}\)


The point \(Q\) is \((-2, 12)\).
The point \(R\) is \((29, 12)\).

Find the column vector \(\overrightarrow{QR}\)


The point \(S\) is \((-0.7, 1.9)\).
The point \(T\) is \((6.9, -8.4)\).

Find the column vector \(\overrightarrow{ST}\)


The point \(U\) is \((8.5, 8.8)\).
The point \(V\) is \((9.9, 9.3)\).

Find the column vector \(\overrightarrow{UV}\)


The point \(W\) is \((-5.2, -3.6)\).
The point \(X\) is \((-5.5, -6.8)\).

Find the column vector \(\overrightarrow{WX}\)


This is Vector Connectors level 3. You can also try:
Level 1 Level 2 Level 4


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Description of Levels


Level 1 - Find the coordinates of a point at the other end of a vector

Level 2 - Find the column vector given the coordinates and a coordinate grid

Level 3 - Find the column vector given the negative vector or larger coordinates

Level 4 - Using vectors to determine if points are collinear

Vectors - Addition and subtraction of vectors and multiplication of a vector by a scalar.

Exam Style Questions - A collection of problems in the style of GCSE or IB/A-level exam paper questions (worked solutions are available for Transum subscribers).

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Curriculum Reference

See the National Curriculum page for links to related online activities and resources.


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