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An online exercise on addition and subtraction of vectors and diagrammatic representations of vectors.

Level 1 Level 2 Level 3 Exam-Style Description Help More Vectors
Vectors with ratios

The diagram shows an irregular hexagon ABCDEF which has vertical and horizontal lines of symmetry.

Opposite sides of the hexagon are parallel.

$$\overrightarrow{ED} = \pmb{g}$$ $$\overrightarrow{DC} = \pmb{h}$$

The diagram is not to scale.

1. Let's begin with a nice easy, straight-forward question. Choose the option below which shows the vector representation of \(\overrightarrow{EC}\) in terms of \(\pmb{g}\) and \(\pmb{h}\).

Correct Wrong

2. Find \(\overrightarrow{BF}\) in terms of \(\pmb{g}\) and \(\pmb{h}\).

Correct Wrong

3. The ratio of FC to ED is 5:2. Find \(\overrightarrow{FC}\) in terms of \(\pmb{g}\).

Correct Wrong

4. Find \(\overrightarrow{EF}\) in terms of \(\pmb{g}\) and \(\pmb{h}\).

Correct Wrong

5. The point M is the midpoint of DC. Find \(\overrightarrow{EM}\) in terms of \(\pmb{g}\) and \(\pmb{h}\).

Correct Wrong

6. The point N lies on ED such that the ratio of EN to ND is 1:2. Find \(\overrightarrow{CN}\) in terms of \(\pmb{g}\) and \(\pmb{h}\).

Correct Wrong

7. The point P lies on FA such that the ratio FP to PA is 4:3. Find \(\overrightarrow{CP}\) in terms of \(\pmb{g}\) and \(\pmb{h}\).

Correct Wrong

8. Find \(\overrightarrow{NP}\) in terms of \(\pmb{g}\) and \(\pmb{h}\).

Correct Wrong

9. Find \(\overrightarrow{PM}\) in terms of \(\pmb{g}\) and \(\pmb{h}\).

Correct Wrong

10. The line AB is extended to X such that the ration AB to AX is 2:7. Find \(\overrightarrow{EX}\) in terms of \(\pmb{g}\) and \(\pmb{h}\).

Correct Wrong

This is Vectors level 3. You can also try:
Level 1 Level 2


Try your best to answer the questions above. Choose one of the five possible answers. When you have finished click the "check" button. If you have any questions wrong, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help.

When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file. You can also claim a 'Transum Trophy' by completing this quiz.

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Description of Levels



Level 1 - Addition and subtraction of vectors and multiplication of vectors by a scalar.

Level 2 - Diagrammatic representations and the modulus of vectors.

Level 3 - Diagrammatic representations and ratios.

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).

Quad Midpoints An Advanced Lesson Starter which can be answered using vectors.

More Vectors A link to the curriculum page for vectors.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

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And now for something completely different. Help the cops catch the robbers by finding the vectors that will end the chase.

Student Activity


The video above is from Maths Genie.

Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly. You can double-click the 'Check' button to make it float at the bottom of your screen.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

Log in Sign up