# What is the projection of <-2,2,5 > onto <1,6,9 >?

Dec 19, 2016

The answer is =55/118〈1,6,9〉

#### Explanation:

The projection of $\vec{b}$ onto $\vec{a}$ is

=(veca.vecb)/(∥veca∥^2)veca

The dot product is =〈-2,2,5〉.〈1,6,9〉

$= \left(- 2 + 12 + 45\right)$

$= 55$

The modulus of $\vec{a}$

=∥〈1,6,9〉∥

$= \sqrt{1 + 36 + 81} = \sqrt{118}$

Therefore,

the projection is

=55/118〈1,6,9〉