If the direction cosines of two lines are given by l+m+n=0 and l^2-5 m^2+n^2=0 , then the angle between them is

Step-by-step solution

Given direction cosines of two lines are aligned & l+m+n=0 & l^2-5 m^2+n^2=0 aligned and Also, aligned l^2+m^2+n^2 & =1 (I₁, m₁, n₁ ) & = (- 2 6 , 1 6 , 1 6 ) aligned and (I₂, m₂, n₂ )= ( 1 6 , 1 6 , -2 6 ) aligned & = |l₁ I₂+m₁ m₂+n₁ n₂ | = & |- 2 6 1 6 + 1 6 1 6 - 2 6 1 6 | & = |- 2 6 + 1 6 - 2 6 |= |- 3 6 | = & 1 2 =60^ = 3 aligned