Question

Let the direction cosines of two lines satisfy the equations : \( 4l + m - n = 0 \) and \( 2mn + 5nl + 3lm = 0 \). Then the cosine of the acute angle between these lines is :

• A. \( \frac{10}{3\sqrt{38}} \)
• B. \( \frac{20}{3\sqrt{38}} \)
• C. \( \frac{10}{7\sqrt{38}} \)
• D. \( \frac{10}{\sqrt{38}} \)

Hint:

For direction cosines, always remember the identity \( l^2 + m^2 + n^2 = 1 \). If you find direction ratios $(a, b, c)$, convert them to cosines using $l = a/\sqrt{a^2+b^2+c^2}$.

Answer 1

The Correct Option is A