The direction cosines of three mutually perpendicular straight lines are l1,m1,n1,l2,m2,n2,l3,m3,n3. Then the direction cosines of a line which is equally inclined to the given three lines, are

Given  l1,m1,n1,l2,m2,n2,l3,m3,n3are the direction cosines of three mutually perpendicular lines It implies that ∑l1l2=∑l2l3=∑l1l3=0,∑l12=∑l22=∑l32=1Hence the direction cosines of line which is equally inclined to the above lines are l1+l2+l33,m1+m2+m33,n1+n2+n33,