Question

The angle between the lines, whose direction cosines \( l, m, n \) satisfy the equations \( l + m + n = 0 \) and \( 2l^{2} + 2m^{2} - n^{2} = 0 \), is

• A. $60^\circ$
• B. $180^\circ$
• C. $90^\circ$
• D. $30^\circ$

Hint:

Geometry Tip: When substituting linear constraints into quadratic direction cosine constraints, if a perfect square like $(l \pm m)^2 = 0$ appears, it implies proportional direction ratios, so the lines are parallel or coincident. Hence, the angle is $0^\circ$ or $180^\circ$.

Answer 1

The Correct Option is B