$\def \u#1{\,\mathrm{#1}}$ $\def \abs#1{\left|#1\right|}$ $\def \ast{*}$ $\def \deg{^{\circ}}$ $\def \ten#1{\times 10^{#1}}$ $\def \redcancel#1{{\color{red}\cancel{#1}}}$ $\def \BLUE#1{{\color{blue} #1}}$ $\def \RED#1{{\color{red} #1}}$ $\def \PURPLE#1{{\color{purple} #1}}$ $\def \th#1,#2{#1,\!#2}$ $\def \lshift#1#2{\underset{\Leftarrow\atop{#2}}#1}}$ $\def \rshift#1#2{\underset{\Rightarrow\atop{#2}}#1}}$ $\def \dotspot{{\color{lightgray}{\circ}}}$

Math with Vector Notation

To multiply or divide a vector by a scalar in this tuple notation, you distribute the scalar over the tuple, multiplying or dividing both components: $$3(1,2)=(3,6)\qquad (3,6)\div3=(1,2)$$

To add two vectors together in this notation, you add the $x$ values and the $y$ values separately: $$(3,2)+(-1,1)=(3-1 ,2+1) = (2,3)$$

The magnitude of a vector $(x,y)$ is $$\abs{(x,y)} = \sqrt{x^2+y^2}$$ For example, the magnitude of the vector (2,3) above is $$\abs{(2,3)} = \sqrt{2^2+3^2} = \sqrt{4+9} = \sqrt{13} \approx 3.6$$