If  3,−1,2,4,1,0are the direction ratios of two straight lines, then which of the following are not direction numbers perpendicular to both these lines?

If  a1,b1,c1,a2,b2,c2are direction ratios of two lines. The direction ratios of any line perpendicular to the above two lines are proportional to the components of the vectors two whose direction ratios areijka1b1c1a2b2c2  Hence,ijka1b1c1a2b2c2=ijk3−12410=i−2−j−8+k7Therefore, the direction ratios of perpendicular line are proportional to  −2,8,7It implies that 32,128,112are not proportional to the above direction ratios.