Explain why there is no plane parallel to the plane 5x3y2z10

Explain why there is no plane parallel to the plane 5x-3y+2z=10 that contains the line with parametrix equations x=t-4 y=3t-2 z=5-2t

for a line to be parallel to plane , it should be inclined at same angle to the co-ordinate spaces; so it should have direction cosines as (5,-3,2) but the line is having (1,3,-2 ) (coefficient of \'t\'); so they cannot be parallel