Vector Basics
Represent displacement using magnitude and direction, and combine vectors geometrically or algebraically.
What is a vector?
A vector has both magnitude and direction. In two dimensions we often write \(\mathbf a=\begin{pmatrix}x\y\end{pmatrix}\). The magnitude is
\[|\mathbf a|=\sqrt{x^2+y^2}.\]
Worked example
If \(\mathbf a=\begin{pmatrix}3\4\end{pmatrix}\), then
\[|\mathbf a|=\sqrt{3^2+4^2}=5.\]
If \(\mathbf b=\begin{pmatrix}-1\2\end{pmatrix}\), then \(\mathbf a+\mathbf b=\begin{pmatrix}2\6\end{pmatrix}\).