# What is the projection of < 5 , -6, 0 > onto < -1, -4 , 6 >?

Aug 23, 2017

see below

#### Explanation:

Use the formula $p r o {j}_{a} b = \frac{a \cdot b}{|} a {|}^{2} a$

That is,
$p r o {j}_{a} b = \frac{< 5 , - 6 , 0 > \cdot < - 1 , - 4 , 6 >}{\sqrt{{5}^{2} + {\left(- 6\right)}^{2} + {0}^{2}}} ^ 2 < 5 , - 6 , 0 >$

$= \frac{- 5 + 24 + 0}{25 + 36} < 5 , - 6 , 0 >$

$= \frac{19}{61} < 5 , - 6 , 0 >$

$= < \frac{95}{61} , - \frac{114}{61} , 0 >$