# Vectors

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

##### Level 1Level 2Level 3Level 4Level 5DescriptionHelpMore Vectors
 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 $$\pmb{h}$$.

 A.     $$\pmb{g+h}$$ B.     $$\pmb{g-h}$$ C.     $$\pmb{h-g}$$ D.     $$\pmb{2g}$$ E.     $$\pmb{g+\frac12 h}$$

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

 A.     $$\pmb{g+h}$$ B.     $$\pmb{g-h}$$ C.     $$\pmb{-g-h}$$ D.     $$\pmb{h-g}$$ E.     $$\pmb{h}$$

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

 A.     $$\pmb{5g}$$ B.     $$\pmb{2g}$$ C.     $$\pmb{7g}$$ D.     $$\pmb{\frac{2}{5}g}$$ E.     $$\pmb{\frac{5}{2}g}$$

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

 A.     $$\pmb{2h-3g}$$ B.     $$\pmb{h-\frac{3}{2}g}$$ C.     $$\pmb{3h-2g}$$ D.     $$\pmb{h-\frac{2}{3}g}$$ E.     $$\pmb{7h-5g}$$

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

 A.     $$\pmb{g + \frac12 h}$$ B.     $$\pmb{h + \frac12 g}$$ C.     $$\pmb{2g + h}$$ D.     $$\pmb{h + 2g}$$ E.     $$\pmb{\frac12 g + \frac12 h}$$

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 $$\pmb{h}$$.

 A.     $$\pmb{-h -g + \frac12 g}$$ B.     $$\pmb{-3g - 2h}$$ C.     $$\pmb{2g - 2h}$$ D.     $$\pmb{-h-\frac23 g}$$ E.     $$\pmb{-h-\frac12 g}$$

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 $$\pmb{h}$$.

 A.     $$\pmb{\frac{3}{4}g + \frac{2}{5}h}$$ B.     $$\pmb{\frac{4}{3}g - \frac{5}{2}h}$$ C.     $$\pmb{\frac{4}{7}g + \frac{5}{2}h}$$ D.     $$\pmb{\frac{4}{7}g - \frac{5}{2}h}$$ E.     $$\pmb{\frac{4}{7}h - \frac{5}{2}g}$$

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

 A.     $$\pmb{11(\frac{h}{7} - \frac{g}{6})}$$ B.     $$\pmb{11(\frac{g}{7} - \frac{h}{6})}$$ C.     $$\pmb{11(\frac{g}{7} + \frac{h}{6})}$$ D.     $$\pmb{11(\frac{h}{7} + \frac{g}{6})}$$ E.     $$\pmb{\frac{11}{7}h + \frac{11}{6}g}$$

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

 A.     $$\pmb{5(\frac{g}{2}+\frac{3h}{14})}$$ B.     $$\pmb{5(\frac{g}{2}-\frac{3h}{14})}$$ C.     $$\pmb{\frac{5g}{2}+\frac{15h}{14}}$$ D.     $$\pmb{5(\frac{h}{2}+\frac{3g}{14})}$$ E.     $$\pmb{\frac{5h}{2}+\frac{15g}{14}}$$

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 $$\pmb{h}$$.

 A.     $$\pmb{\frac{2}{7}h + \frac{2}{5}g}$$ B.     $$\pmb{7h-5g}$$ C.     $$\pmb{-h-\frac12 g}$$ D.     $$\pmb{\frac{5h}{2}+\frac{15g}{14}}$$ E.     $$\pmb{2(g+h)}$$

This is Vectors level 3. You can also try:
Level 1 Level 2 Level 4 Level 5

## Instructions

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.

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#### Strategy Games

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## Go Maths

Learning and understanding Mathematics, at every level, requires learner engagement. Mathematics is not a spectator sport. Sometimes traditional teaching fails to actively involve students. One way to address the problem is through the use of interactive activities and this web site provides many of those. Click here for more activities designed for students in upper Secondary/High school.

## Teachers

If you found this activity useful don't forget to record it in your scheme of work or learning management system. The short URL, ready to be copied and pasted, is as follows:

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## Description of Levels

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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.

Level 4 - GCSE style exam questions

Level 5 - IB and A Level style questions

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.

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

Transum.org/go/?to=Vectorcops

## Example

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.

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