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

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Answer 1 · 2016-12-20T09:38:36

The answer is $=34/41〈3,-4,4〉$

The vector projection of $vecb$ onto $veca$ is

$=(veca.vecb)/(∥veca∥^2)veca$

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

$=(6-12-28)=34$

The modulus of $veca$ is $=∥veca∥=∥〈3,-4,4〉∥$

$=sqrt(9+16+16)=sqrt41$

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

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