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

# 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

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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

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## Example

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