# What is the projection of < -1, 5, 7> onto < 7,-3, -5>?

Dec 21, 2016

The answer is =-57/83〈7,-3,-5〉

#### Explanation:

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

=(veca.vecb)/(∥veca∥^2)veca

The dot product is veca.vecb=〈-1,5,7〉.〈7,-3,-5〉

$= \left(- 7 - 15 - 35\right) = - 57$

The modulus of $\vec{a}$ is =∥veca∥=∥〈7,-3,-5〉∥

$= \sqrt{49 + 9 + 25} = \sqrt{83}$

The vector projection is =-57/83〈7,-3,-5〉