# How do you find the projection of u=<4,8> onto v=<-1,2>?

May 28, 2017

$\left(- \frac{12}{5} , \frac{24}{5}\right)$

#### Explanation:

$u \cdot v = | | u | | \cdot | | v | | \cdot \cos \theta$

But you want $| | u | | \cdot \cos \theta \cdot \hat{v} = \frac{u \cdot v}{| | v | |} \cdot \frac{v}{| | v | |} = \frac{u \cdot v}{v \cdot v} \cdot v$

$= \frac{4 \left(- 1\right) + 8 \cdot 2}{{\left(- 1\right)}^{2} + {2}^{2}} \cdot \left(- 1 , 2\right)$

$= \frac{12}{5} \cdot \left(- 1 , 2\right)$