__Scalars Vs. Vectors__

Criteria |
Scalar |
Vector |

Definition | A scalar is a quantity with magnitude only. | A vector is a quantity with magnitude and direction. |

Direction | No | Yes |

Specified by | A number (magnitude) and a unit | A number (magnitude), direction and a unit |

Represented by | quantity’s symbol | quantity’s symbol in bold or an arrow sign above |

Example | mass, temperature | velocity, acceleration |

__Position and Displacement Vectors__

**Position Vector:** Position vector of an object at time t is the position of the object relative to the origin. It is represented by a straight line between the origin and the position at time t.

**Displacement Vector:** Displacement vector of an object between two points is the straight line between the two points irrespective of the path followed. The path length is always equal or greater than the displacement.

__Free and Localized Vectors__

A **free vector**(or non-localized vector) is a vector of which only the magnitude and direction are specified, not the position or line of action. Displacing it parallel to itself leaves it unchanged.

A **localized vector** is a vector where line of action and position are as important as magnitude and direction. These vectors change with change in position and direction.