Question

What is the projection of `<6,0,3 >` onto `<2,5,-7 >`?

Answer 1

The vector projection is `〈-9/39,-45/78,63/78〉`

Explanation:

Let `vecb=〈6,0,3〉`

and `veca=〈2,5,-7〉`

The dot product is `veca.vecb=(6*2+5*0+3*-7)=12-21=-9`

`∣veca∣^2= (4+25+49)=78`

So the projection is
`(veca.vecb)veca / (∣veca∣^2)=-9/78 〈2,5,-7〉`