\(\def \u#1{\,\mathrm{#1}}\) \(\def \abs#1{\left|#1\right|}\) \(\def \ast{*}\) \(\def \deg{^{\circ}}\) \(\def \ten#1{\times 10^{#1}}\) \(\def \redcancel#1{{\color{red}\cancel{#1}}}\) \(\def \BLUE#1{{\color{blue} #1}}\) \(\def \RED#1{{\color{red} #1}}\) \(\def \PURPLE#1{{\color{purple} #1}}\) \(\def \th#1,#2{#1,\!#2}\) \(\def \lshift#1#2{\underset{\Leftarrow\atop{#2}}#1}}\) \(\def \rshift#1#2{\underset{\Rightarrow\atop{#2}}#1}}\) \(\def \dotspot{{\color{lightgray}{\circ}}}\)
Appendix B: Vectors
5.

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: $$3(1,2)=(3,6)\qquad (3,6)\div3=(1,2)$$
(no alternate text)

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 $$\abs{(2,3)} = \sqrt{2^2+3^2} = \sqrt{4+9} = \sqrt{13} \approx 3.6$$