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

Oct 27, 2016

The projection is 〈11/27,55/27,99/27〉

#### Explanation:

Let vecb=〈-6,1,5〉 and veca=〈1,5,9〉

Then, the vector projection of $\vec{b}$ onto $\vec{a}$ is given by

(veca.vecb)/(∣veca∣∣veca∣)*veca

$\vec{a} . \vec{b}$ is the dot product
and ∣veca∣ is the modulus of the vector

the dot product is veca.vecb=〈1,5,9〉.〈-6,1,5〉=-6+5+45=44

∣veca∣= sqrt(1^2+5^2+9^2)=sqrt(1+25+82)=sqrt108

so the projection =(44/108)〈1,5,9〉=(11/27)〈1,5,9〉=〈11/27,55/27,99/27〉