To calculate del . r (A . r), where A is a constant vector and r is a distance vector, one must apply vector calculus principles. The dot product and divergence operations are key to solving this equation. The result of the operation should yield 4(r.A), indicating a relationship between the divergence and the dot product of the vectors involved. Understanding the properties of vector fields and applying the product rule for divergence will aid in finding the solution. Mastering these concepts is essential for accurate calculations in vector calculus.