Question

If \( l_1, m_1, n_1 \) and \( l_2, m_2, n_2 \) are direction cosines of lines \( L_1 \) and \( L_2 \) respectively and \( \theta \) is the acute angle between them, then :

• A. \( \cos \theta = l_1l_2 + m_1m_2 + n_1n_2 \)
• B. \( \sin \theta = l_1l_2 + m_1m_2 + n_1n_2 \)
• C. \( \tan \theta = \frac{l_1}{l_2} + \frac{m_1}{m_2} + \frac{n_1}{n_2} \)
• D. \( \cos \theta = |l_1l_2 + m_1m_2 + n_1n_2| \)

Hint:

Whenever a question specifies an "acute angle" between lines in 3D geometry, always look for the option containing the absolute value modulus sign to ensure the output value is positive.

Answer 1

The Correct Option is D