# What is the projection of <-2,4,2 > onto <1,8,-3 >?

Oct 14, 2017

The projection is $= \frac{12}{37} < 1 , 8 , - 3 >$

#### Explanation:

Let the vectors be

$\vec{u} = < - 2 , 4 , 2 >$

and

$\vec{v} = < 1 , 8 , - 3 >$

The projection of $\vec{u}$ onto $\vec{v}$ is

$p r o {j}_{\vec{v}} \vec{u} = \frac{\vec{u} . \vec{v}}{| | \vec{v} | {|}^{2}} \vec{v}$

$= \frac{< - 2 , 4 , 2 > . < 1 , 8 , - 3 >}{| | < 1 , 8 , - 3 > | {|}^{2}} < 1 , 8 , - 3 >$

$= \frac{- 2 + 32 - 6}{1 + 64 + 9} < 1 , 8 , - 3 >$

$= \frac{24}{74} < 1 , 8 , - 3 >$

$= \frac{12}{37} < 1 , 8 , - 3 >$