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

# Vectors

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

##### MenuConnectLevel 1Level 2Level 3Level 4Level 5ExamHelpMore
 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 ratio 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.     $$\pmb{\frac{5}{2}g + 2h}$$ ✓ ✗
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This is Vectors level 5. You can also try:
Vector Connectors Level 1 Level 2 Level 3 Level 4

## 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.

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## 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).

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## 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.

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