The equation of a line passing through the point on z-axis at a distance of 1 unit from the origin and having direction ratios 1,0,−1 is

The coordinates of the point which are on  z-axis and at a distance of  1 units from the origin is 0,0,1 Therefore, the equation of the line passing through the point  0,0,1and parallel to the line whose direction ratio are 1,0,−1 is   x−01=y−00=z−1−1