# What is the projection of <3 ,-4, 7 > onto < -1 , 9,-2 >?

Dec 22, 2016

The answer is =-53/86〈-1,9,-2〉

#### Explanation:

The vector projection of $\vec{b}$ over $\vec{a}$ is

=(veca-vecb)/(∣veca∣^2)*veca

The dot product is

veca.vecb=〈3,-4,7〉.〈-1,9,-2〉=(-3-36-14)=-53

The modulus of $\vec{a}$ is =∣〈-1,9,-2〉∣=sqrt(1+81+4)=sqrt86

The vector projection is

=-53/86〈-1,9,-2〉