The equation of the line passing through the point (a,b,c)  and parallel to z− axis is

The equation of the line passing through the point(x1,y1,z1)  and parallel to the line whose direction ratios are ⟨a,b,c⟩ is x−x1a=y−y1b=z−z1cThe direction cosines of z−axis ⟨0,0,1⟩  Therefore, the equation of the line passing through the point (a,b,c)  and parallel to the line whose direction ratio are ⟨0,0,1⟩  is x−a0=y−b0=z−c1