# What is the projection of < 6 , -6 ,3 > onto < 4, -5, 1>?

Mar 14, 2016

=$< \frac{228}{42} , \frac{- 285}{42} , \frac{57}{42} >$

#### Explanation:

Projection of a vector a on another vector b (component of a along b )is given by

$P r o {j}_{b} a$ = $\frac{\ast a \ast . \ast b \ast}{|} | b | {|}^{2} \ast b \ast$
Hence if a is <6,-6,3> and b is < 4,-5,1>
a . b = 24 +30 +3 =57

$| | b | {|}^{2} = {4}^{2} + {\left(- 5\right)}^{2} + {1}^{2}$=42

Hence,$P r o {j}_{b} a = \frac{57}{42} < 4 , - 5 , 1 >$

=$< \frac{228}{42} , \frac{- 285}{42} , \frac{57}{42} >$