Question

What is the projection of `< 0 , 2, -2 >` onto `< 3 , -7, 4 >`?

Answer 1

`<-66/74, 154/74, 88/74>`

Explanation:

Projection of a given vector u on another vector v is the scalar multiple of vector v, given by the formula
`proj_v u =(vec u . vec v)/|vec v|^2 vec v`

The required projection would thus be `(0.3 -2.7-2.4)/ (3^2 +7^2 +4^2) <3,-7,4>`

=`-22/74 <3,-7,-4>`

=`<-66/74, 154/74, 88/74>`