# What is the projection of < 0 , 2, -2 > onto < 3 , -7, 4 >?

Mar 24, 2016

$< - \frac{66}{74} , \frac{154}{74} , \frac{88}{74} >$

#### Explanation:

Projection of a given vector u on another vector v is the scalar multiple of vector v, given by the formula
$p r o {j}_{v} u = \frac{\vec{u} . \vec{v}}{|} \vec{v} {|}^{2} \vec{v}$

The required projection would thus be $\frac{0.3 - 2.7 - 2.4}{{3}^{2} + {7}^{2} + {4}^{2}} < 3 , - 7 , 4 >$

=$- \frac{22}{74} < 3 , - 7 , - 4 >$

=$< - \frac{66}{74} , \frac{154}{74} , \frac{88}{74} >$