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# Chapter 3 - Vectors

## Vectors and scalars

Vector quantities with number, **direction** and units:

Displacement $\vec{r}$ [m]

Velocity $\vec{v}$ [ms^{-1}]

Acceleration $\vec{a}$ [ms^{-2}]

Scalar quantities number and units only

Distance traveled [m]

Speed [ms^{-1}]

## Graphical representation of vectors and components

It is frequently useful to draw two dimensional vectors as arrows, and to split them in to components that lie along the coordinate axes. The choice of coordinate axes is up to you..but choosing the right ones will make the problem easier or harder.

We can take a look at the acceleration due to gravity as vector using a phone accelerometer, using this tool (click on the link from your phone's browser).

## Adding and subtracting vectors

## Vectors - Components

$v_{1x}=v_{1}\cos\theta_{1}$ | $v_{2x}=v_{2}\cos\theta_{2}$ |

$v_{1y}=v_{1}\sin\theta_{1}$ | $v_{2y}=v_{2}\sin\theta_{2}$ |

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$v_{Rx}=v_{1x}+v_{2x}$ | $\tan\theta_{R}=\frac{v_{Ry}}{v_{Rx}}$ |

$v_{Ry}=v_{1y}+v_{2y}$ | $v_{R}=\sqrt{v_{Rx}^2+v_{Ry}^2}$ |