Question

Define vector and state two examples.

Answer 1

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:

`\begin{gathered} \vec{v}=ai+bj=4i+3j\\ \\ \vec{v}=<4,3> \end{gathered}`

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:

`\begin{gathered} \vec{v}=ai+bj\\ \\ magnitude:\\ \\ |\vec{v}|=√(a^2+b^2)\\ \\ angle:\\ \\ \theta=\tan^(-1)((b)/(a)) \end{gathered}`