If the direction cosines of two lines are connected by the relations l+m+n=0  and  2nl+2lm−mn=0, then the direction cosines of the two lines are

Suppose that n=−1Hence the equations become l+m=1and−2l+2lm+m=0Substitute m=1−l in the equation  −2l+2lm+m=0  and then solve for lIt implies that2l2+l−1=0Hence, l=−1,12it implies thatm=2,12Therefore, the direction ratios are −1,2,−1,1,1,−2The direction cosines are−16,26,−16,16,16,−26