# How do you find the projection of u=<62,21> onto v=<-12,4>?

Jun 18, 2017

$x \cdot \hat{v}$ below

#### Explanation:

Scalar product: $u \cdot v = | u | \cdot | v | \cdot \cos \theta$

But the projection is the $\hat{v}$ multiplied by the scalar horizontal leg: $\cos \theta = \frac{x}{|} u |$

Therefore $x \hat{v} = | u | \cdot \cos \theta \cdot \frac{v}{|} v | = | u | \cdot \frac{\left(u \cdot v\right)}{| u | \cdot | v |} \cdot \frac{v}{|} v |$

$\left(u \cdot v\right) = - 62 \cdot 12 + 21 \cdot 4 = - 660$

$\left(v \cdot v\right) = {12}^{2} + {4}^{2} = 160$

$x \hat{v} = - \frac{660}{160} \cdot \left(- 12 , 4\right) = \left(\frac{99}{2} , - \frac{33}{2}\right)$