Question:
If the direction cosines of two lines are given by
\[
l + m + n = 0 \quad \text{and} \quad mn - 2lm - 2nl = 0,
\]
then the acute angle between those lines is:
If the direction cosines of two lines are given by
\[
l + m + n = 0 \quad \text{and} \quad mn - 2lm - 2nl = 0,
\]
then the acute angle between those lines is:
Show Hint
Use trigonometric properties to solve for angles when given direction cosine relations.
Updated On: Mar 13, 2025
- \( \frac{2\pi}{5} \)
- \( \frac{\pi}{3} \)
- \( \frac{\pi}{4} \)
- \( \frac{\pi}{60} \)
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The Correct Option is B
Solution and Explanation
Step 1: Solve for direction cosines
Given:
\[
l + m + n = 0.
\]
We solve using the second equation:
\[
mn
- 2lm
- 2nl = 0. \] Substituting values, solving for angles, we find: \[ \cos \theta = \frac{1}{2}. \] Step 2: Compute the angle \[ \theta = \cos^{
-1} \frac{1}{2} = \frac{\pi}{3}. \]
- 2lm
- 2nl = 0. \] Substituting values, solving for angles, we find: \[ \cos \theta = \frac{1}{2}. \] Step 2: Compute the angle \[ \theta = \cos^{
-1} \frac{1}{2} = \frac{\pi}{3}. \]
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