# Vector and Scalar Quantities, Vector Addition, and Vector Components

## Vector and Scalar Quantities

### Scalar

A scalar quantity is specified completely by its magnitude, that's a number and a unit.

Examples are speed (75 km/h, 55 mph), Distance (50 km, 10 feet), Volume (500 cm^{3}, 45 feet^{3}).

Scalar quantities that are measured in the same units may be added or subtracted in the usual way.

For example:

23mm + 7mm = 30 mm

54 m^{2} − 5 m^{2} = 49 m^{2}

### Vector

A vector quantity is specified completely by a magnitude and a direction.

It consists of a number, a unit, and a direction.

Examples are displacement (35 m, North) and velocity (70 km/h, 30° North of East).

The direction must be a part of any calculations involving vector quantity.

See example below in which the figure shows the direction of a vector by reference to North (N), South (S), East (E), and West (W).

Vectors are different from scalars:

- Vectors must be represented by: a magnitude + direction + units.

Scalars can be represented by: magnitude + units.
- Vectors can be added or subtracted using special methods.

Scalars can be added or subtracted simply using arithmetics operations.

### Exercise with Solution: Vector or Scalar

Specify which one is vector or scalar:
15 m |
_________________ |

55 m/s, North |
_________________ |

15 km, South |
_________________ |

25 degrees Celsius |
_________________ |

10 exabytes |
_________________ |

100 calories |
_________________ |

Check your answers here:
*Specify which one is vector or scalar*
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Date of last modification: 2024