# Vectors

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

##### Level 1Level 2Level 3Exam-Style Description Help More 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

## 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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## Transum.org

This web site contains hundreds of free mathematical activities for teachers and students. Click here to go to the main page which links to all of the resources available.

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Comment recorded on the 1 May 'Starter of the Day' page by Phil Anthony, Head of Maths, Stourport High School:

"What a brilliant website. We have just started to use the 'starter-of-the-day' in our yr9 lessons to try them out before we change from a high school to a secondary school in September. This is one of the best resources on-line we have found. The kids and staff love it. Well done an thank you very much for making my maths lessons more interesting and fun."

Comment recorded on the 14 September 'Starter of the Day' page by Trish Bailey, Kingstone School:

"This is a great memory aid which could be used for formulae or key facts etc - in any subject area. The PICTURE is such an aid to remembering where each number or group of numbers is - my pupils love it!
Thanks"

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#### Tran Towers

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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

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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.

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.

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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