Vectors and scalars
Vector – this is a quantity that has a size and direction (e.g. displacement, velocity, force)
Scalar – a quantity with a size or magnitude only (e.g. length, speed, mass)
When representing vectors, the magnitude is given by the length of the line and the direction is given by the arrow on the line.
For example, the vector below is represented as a column vector as follows:
AB – represent the direction
6 – is the horizontal unit of movement
3 – is the vertical unit of movement
The negative of a vector
A negative or inverse vector is represented as:
This vector is represented as:
The zero and unit vector
A vector with a magnitude of 0 is called the zero vector and vector with a magnitude of 1 is called a unit vector.
The unit base vectors
Column vectors can easily be written in terms of i and j. For example,
In the example above, the number of i’s demonstrates how many units are moved horizontally and the number of j’s demonstrates how many units are moved vertically.