# What is the projection of <8,-1,6 > onto <-1,5,-3 >?

Oct 21, 2016

The vector projection is 〈-31/35,-31/7,93/35〉

#### Explanation:

Let vecb=〈8,-1,6〉

and veca=〈-1,5,-3〉

Then the vector projection of $\vec{b}$ onto $\vec{a}$ is
=(veca.vecb)/(∣veca∣)^2*veca
where the dot product is $\vec{a} . \vec{b}$

dot product $\left(8 \cdot - 1\right) + \left(- 1 \cdot 5\right) + \left(6 \cdot - 3\right) = - 8 - 5 - 18 = - 31$

and (∣veca∣)^2=(1+25+9)=35

so the projection is -31/35〈-1,5,-3〉 =〈-31/35,-31/7,93/35〉