# 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, N) and velocity (70 km/h, 30° N of E).

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 only: magnitude + units.
- Vectors can be added and subtracted using special methods.

Scalars can be added or subtracted simple using algebraic summation.

### Exercise with Solution: Vector or Scalar

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

55 m/sec, 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: 2022