If A is a constant vector, prove that del (r.A) = A

Question

The question is taken from the book of vector analysis by Schaum's outlines.

Answer 1

r=<x,y,z>; A=<a,b,c> where a, b and c are constants.

r.A=ax+by+cz; del(r.A)=<∂(r.A)/∂x,∂(r.A)/∂y,∂(r.A)/∂z)>=

<∂(ax+by+cz)/∂x,∂(ax+by+cz)/∂y,∂(ax+by+cz)/∂z)>=<a,b,c>=A QED.