# What is the projection of  (2i -3j + 4k) onto (- 5 i + 4 j - 5 k)?

Jan 2, 2017

The answer is =-7/11〈-5,4,-5〉

#### Explanation:

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

=(veca.vecb)/(∣veca∣)^2veca

The dot product is

veca.vecb=〈2,-3,4〉.〈-5,4,-5〉=(-10-12-20)=-42

The modulus of $\vec{a}$ is =∣〈-5,4,-5〉∣

$= \sqrt{25 + 16 + 25} = \sqrt{66}$

The vector projection is =-42/66〈-5,4,-5〉

=-7/11〈-5,4,-5〉