Hello Jeroen,
what exactly do you mean with "from components"?
This perhaps?
res2a = my Table[(3 r[i] r[j] - Sum[r[i]^2, {i, 1, 3}] KroneckerDelta[i, j])/(Sqrt[Sum[r[i]^2, {i, 1, 3}]])^5, {i, 1, 3}, {j, 1, 3}]
And for better comparison with former res2
res2a /. {r[1] -> r1, r[2] -> r2, r[3] -> r3} // MatrixForm