The solution to the problem is as mentioned by @chris in comments of the question
Replace the VectorPlot3D[] command which is
VectorPlot3D[Grad[rint3[x, y, z], {x, y, z}],
{x, -2, 2}, {y, -2, 2}, {z, -2, 2}]
by
VectorPlot3D[Grad[rint3[x, y, z], {x, y, z}]//Evaluate,
{x, -2, 2}, {y, -2, 2}, {z, -2, 2}]
"//Evaluate" command has been added.
The output will be
