# Vectors

A vector quantity has both length (magnitude) and direction. The opposite is a scalar quantity, which only has magnitude. Vectors can be denoted by AB, a, or AB (with an arrow above the letters).
If a = (3) then the vector will look as follows:
(2)

NB1: When writing vectors as one number above another in brackets, this is known as a column vector.
NB2: in textbooks and here, vectors are indicated by bold type. However, when you write them, you need to put a line underneath the vector to indicate it.

Example:
If a = (-5) and b = ( 2), find the magnitude of their resultant.
( 3) (1)

The resultant of two or more vectors is their sum.
The resultant therefore is (-3).
( 4)
The magnitude of this is (-3² + 4²) = (9 + 16) = (25) = 5

The addition and subtraction of vectors can be shown diagrammatically. To find a + b, draw a and then draw b at the end of a. The resultant is the line between the start of a and the end of b.
To find a - b, find -b (see above) and add this to a.

Example: