What is a Vector?

Scalar quantities are quantities that have only magnitudes such as time, area and distance.

Vector quantities are quantities that have both magnitudes and directions such velocity (speed and direction), force and acceleration.

A vector can be represented by a directed line segment, whose direction is given by the arrow and the length shows the magnitude of the vector.

The vectors can be denoted by or AB or or or a.

A is called the initial point and B is called the terminal point of .

The magnitude of a vector is the length of the corresponding segment. The magnitude of is denoted by .

A vector can be written as an ordered pair called a column vector.

Consider the line PQ in the diagram. The line represents the translation of P to Q, which is 2 right and 3 up.

This can be written as the ordered pair

Example:

Express as a column vector.

Solution:

The translation of C to D is 4 right and 3 down.

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