...Given that three vectors , are perpendicular to each other (where are not and given that , show that p=q=r=0.

I get the solution, but I don't understand something written in my solution book.

It says

Since <<<<< the result is the nullvectorwhich is perpendicular to any other vector

<<<<<< since the null vector is perpendicular to any other vector the scalar (dot) product must be zero. (A dot product yields a real number not a vector!)

Notice that in the second line it is just 0, not

Why?