# How do you find the scalar and vector projections of b onto a given a = <3, -6, 2>, b = <1, 1, 1>?

Nov 14, 2016

The scalar projection is $= - \frac{1}{7}$
The vector projection is =-1/49〈3,-6,2〉

#### Explanation:

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

=(veca.vecb)/(∥veca∥)

veca=〈3,-6,2〉

vecb=〈1,1,1〉

veca.vecb=〈3,-6,2〉.〈1,1,1〉=3-6+2=-1

∥veca∥=∥〈3,-6,2〉∥=sqrt(9+36+4)=sqrt49=7

The scalar projection is $= - \frac{1}{7}$

The vector projection is (veca.vecb)/(∥veca∥)^2veca

=-1/49〈3,-6,2〉