Notes
A vector has magnitude and direction: $\vec v=\langle a,b\rangle$.
- Magnitude: $\displaystyle |\vec v|=\sqrt{a^2+b^2}$.
- Add componentwise; scalar multiples stretch.
- Dot product: $\langle a,b\rangle\cdot\langle c,d\rangle=ac+bd$; zero means perpendicular.
- Unit vector: $\displaystyle \frac{\vec v}{|\vec v|}$.
Practice
$|\langle 6,8\rangle|=$
$\displaystyle \sqrt{36+64}$.
$\langle1,2\rangle+\langle3,-5\rangle=$
Add components.
$\langle2,3\rangle\cdot\langle3,-2\rangle=$
$6-6=0$, so they're perpendicular.
Ready for more? Take the Unit 4 test.