Common Vector Operations

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> lets you 'project' one vector on to another

That's one the the areas I can't get to grips with. I have seen terms such as, "we need to project vec1 onto vec2 and use the resulting 'normal' to do ... blah"
Other times its, "We project vec1 onto vec2 and use the resulting projection vector to do ... blah"

Example. If the RED and GREEN lines are vectors and the yellow lines represent the vector normals, what would the results be for projecting RED's normal onto GREEN's?