The acute angle between the two lines whose direction ratios are connected by l+m−n=0  and  l2+m2−n2=0 is

Suppose that n=1Hence the equations become l+m=1and l2+m2=1Substitute m=1−l in the equation  l2+m2=1and then solve for lIt implies that l=1,0 and m=0,1Therefore, the direction ratios are 1,0,1,0,1,1If θ is the acute angle between two lines having direction ratios a1,b1,c1and a2,b2,c2 then cosθ=a1a2+b1b2+c1c2a12+b12+c12⋅a22+b22+c22Suppose that θ be the angle between the lines whose direction ratios are 1,0,1,0,1,1Then cosθ=122=12Therefore, the measure of angle θ is π3