# What is the projection of <4,0,1 > onto <6,-3,7 >?

Dec 23, 2016

The answer is =31/94〈6,-3,7〉

#### Explanation:

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

=(veca.vecb)/(∥veca∥)^2veca

The dot product is $= \vec{a} . \vec{b}$
=〈4,0,1〉.〈6,-3,7〉=(24+0+7)=31

The modulus of $\vec{a}$ is =∥veca∥=∥〈6,-3,7〉∥

$= \sqrt{36 + 9 + 49} = \sqrt{94}$

The vector projection is =31/94〈6,-3,7〉