A vector is a physical quantity that can be measured (has magnitude in units) and also operates in a particular direction, unlike a scalar which can only be measured. Examples of vectors include velocity, acceleration, force and momentum.
A vector can be represented by a line drawn, such that:
- the length of the line represents the <spanclass="texhtml"><em><strong>magnitude</strong></em></span> of the vetor in a given unit;
- the direction of the line represents the <spanclass="texhtml"><em><strong>direction</strong></em></span> in which the vector operates (or acts).
In the figure above, the displacement of A to B is written as <spanclass="texhtml"><strong> AB</strong></span> (<spanclass="texhtml"><strong>ā</strong></span> or <spanclass="texhtml"><strong>a</strong></span>). point A is the origin or initial point and the point B is the head or terminal point. This displacement is equivalent to moving a distance <spanclass="texhtml"><em>x</em></span> horizontally followed by<spanclass="texhtml"><em> y</em></span> vertically.
### The Modulus of a vector
The modulus of a vector is a positive scalar number that gives magnitude of the vector. It is written like this:
<pre><spanclass="texhtml">|<strong>AB</strong>|</span> or <spanclass="texhtml">|<strong>a</strong>|</span> or simply <spanclass="texhtml"><strong>AB</strong></span> or <spanclass="texhtml"><strong>a</strong></span>. </pre>