Equation of line passing through  1,−1,0and parallel to the line having direction cosines 32,0,12  is

The equation of the line passing through the point  x1,y1,z1and parallel to the line whose direction ratios area,b,c isx−x1a=y−y1b=z−z1cHere the direction cosines are 32,0,12 , it implies that the direction ratios are3,0,1Therefore, the equation of the line passing through the point 1,−1,0and having direction ratios 3,0,1 is  x−13=y+10=z1