# What is the projection of <8,2,1 > onto <9,6,3 >?

Dec 21, 2016

The answer is =87/126〈9,6,3〉

#### Explanation:

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

=(veca.vecb)/(∥veca∥^2)veca

The dot product is veca.vecb=〈8,2,1〉.〈9,6,3〉

$= \left(72 + 12 + 3\right) = 87$

The modulus of $\vec{a}$ is =∥veca∥=∥〈9,6,3〉∥

$= \sqrt{81 + 36 + 9} = \sqrt{126}$

The vector projection is =87/126〈9,6,3〉