# What is the projection of  <0,8,5> onto <1,2,-4>?

Apr 26, 2016

$- \frac{4}{\sqrt{21}}$

#### Explanation:

The projection of a vector $A$ along a direction $\theta$ with itself is given as $| A | \cos \theta$

Lets say here $A = < 0 , 8 , 5 >$
And $B = < 1 , 2 , - 4 >$

Their dot product is $| A | | B | \cos \theta = 0 + 16 - 20 = - 4$

So the projection is $\frac{| A | | B | \cos \theta}{| B |} = \frac{- 4}{\sqrt{{1}^{2} + {2}^{2} + {4}^{2}}} = - \frac{4}{\sqrt{21}}$