Vector is a mathematical entity that has a magnitude and a direction.
It is graphically represented by an arrow. The size of the arrow indicates the magnitude, and the tip of the arrow indicates the direction.
For example, we have the vector below:
Some forms of writing this vector are:
[tex]\begin{gathered} \vec{v}=ai+bj=4i+3j\\ \\ \vec{v}=<4,3> \end{gathered}[/tex]Now, let's write a second example of a vector with 6 units in horizontal direction and -4 units in vertical direction, starting at the origin:
The magnitude and angle of a vector are given by:
[tex]\begin{gathered} \vec{v}=ai+bj\\ \\ magnitude:\\ \\ |\vec{v}|=\sqrt{a^2+b^2}\\ \\ angle:\\ \\ \theta=\tan^{-1}(\frac{b}{a}) \end{gathered}[/tex]
