$$\newcommand\mycolv[1]{\begin{pmatrix}#1\end{pmatrix}}$$

# Vectors

## An online exercise on addition and subtraction of vectors and multiplication of a vector by a scalar.

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Vectors can be expressed in terms of other vectors that are equivalent. Here are some examples from the diagram above: $$c=a+b$$  and   $$a=c-b$$  and   $$b=-a+c$$

 1 Which vector is equivalent to$$f+d$$ ? ☐ ☐ ✓ ✗ 2 Which vector is equivalent to$$m+l$$ ? ☐ ☐ ✓ ✗ 3 Which vector is equivalent to$$n+k$$ ? ☐ ☐ ✓ ✗ 4 Which vector is equivalent to$$e-d$$ ? ☐ ☐ ✓ ✗ 5 Which vector is equivalent to$$n-l$$ ? ☐ ☐ ✓ ✗ 6 Which vector is equivalent to$$j-k$$ ? ☐ ☐ ✓ ✗ 7 Express the vector $$e$$ usingtwo other vectors. ☐ ☐ ✓ ✗ 8 Express the vector $$g$$ usingtwo other vectors. ☐ ☐ ✓ ✗ 9 Express the vector $$h$$ usingtwo other vectors. ☐ ☐ ✓ ✗ 10 Express the vector $$j$$ usingtwo other vectors. ☐ ☐ ✓ ✗ 11 Express the vector $$d$$ usingtwo other vectors. ☐ ☐ ✓ ✗ 12 Express the vector $$k$$ usingthree other vectors. ☐ ☐ ✓ ✗
Check

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

## Instructions

Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, 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.

## More Activities:

Mathematicians are not the people who find Maths easy; they are the people who enjoy how mystifying, puzzling and hard it is. Are you a mathematician?

Comment recorded on the 10 April 'Starter of the Day' page by Mike Sendrove, Salt Grammar School, UK.:

"A really useful set of resources - thanks. Is the collection available on CD? Are solutions available?"

Comment recorded on the 24 May 'Starter of the Day' page by Ruth Seward, Hagley Park Sports College:

"Find the starters wonderful; students enjoy them and often want to use the idea generated by the starter in other parts of the lesson. Keep up the good work"

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#### Connect 4 Factors

A mathematical version of the popular Connect 4 game based on getting four numbers with a common factor in a line. Fun for one, two or a whole class of pupils.

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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. The Go Maths page is an alphabetical list of free activities designed for students in Secondary/High school.

## Maths Map

Are you looking for something specific? An exercise to supplement the topic you are studying at school at the moment perhaps. Navigate using our Maths Map to find exercises, puzzles and Maths lesson starters grouped by topic.

## Teachers

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Scan the QR code below to visit the online version of this activity.

https://www.Transum.org/go/?Num=459

## Description of Levels

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Vector Connectors - A basic set of exercises on vectors which could be done before attempting the following.

Level 1 - Addition and subtraction of vectors

Level 2 - Multiplication of vectors by a scalar.

Level 3 - Equivalent vectors as seen in a diagram

Level 4 - The Tangram containing vactors

Level 5 - An irregular hexagon defined by vectors

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).

More on this topic including lesson Starters, visual aids, investigations and self-marking exercises.

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.

## Curriculum Reference

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

## Example

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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