# What is the projection of (2i + 3j – 7k) onto  (3i – 4j + 4k)?

Dec 20, 2016

The answer is =34/41〈3,-4,4〉

#### Explanation:

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

=(veca.vecb)/(∥veca∥^2)veca

The dot product is veca.vecb=〈2,3,-7〉.〈3,-4,4〉

$= \left(6 - 12 - 28\right) = 34$

The modulus of $\vec{a}$ is =∥veca∥=∥〈3,-4,4〉∥

$= \sqrt{9 + 16 + 16} = \sqrt{41}$

The vector projection is =34/41〈3,-4,4〉