I tried solving it again and i calculated that the Jacobian is

| 0 -1 0 |

| 1 0 0 |

J= | 0 0 1 |

| 0 0 0 |

| 0 0 0 |

| 0 0 0 |

whereas the angular velocity is zero so Jw (omega) is zero and the linear velocity is

| 0 -1 0 |

| 1 0 0 |

| 0 0 1 |

for the Zo Z1 and Z2 are 0 1 0, -1 0 0 , and 0 0 1 each.

Let me know if this is not right. The forwards kinematics T3 final table is

| 0 0 -1 -d3 |

| 0 1 0 d2 |

| 1 0 0 d1 |

| 0 0 0 1 |

which therefore shows that the Jacobian is completely not dependent on the prismatic links length.