And are direction cosines of the two lines inclined to each other at an angle

MATHEMATICS · Single correct · CBSE · Mathematics · Three-Dimensional Geometry · Three-Dimensional Geometry

Problem

l_1, m_1, n_1

and

l_2, m_2, n_2

are direction cosines of the two lines inclined to each other at an angle

\theta

, then the direction cosines of the internal bisector of the angle between these lines are (1)

\frac{l_1 + l_2}{2 \sin \frac{\theta}{2}}, \frac{m_1 + m_2}{2 \sin \frac{\theta}{2}}, \frac{n_1 + n_2}{2 \sin \frac{\theta}{2}}

(2)

\frac{l_1 + l_2}{2 \cos \frac{\theta}{2}}, \frac{m_1 + m_2}{2 \cos \frac{\theta}{2}}, \frac{n_1 + n_2}{2 \cos \frac{\theta}{2}}

(3)

\frac{l_1 - l_2}{2 \sin \frac{\theta}{2}}, \frac{m_1 - m_2}{2 \sin \frac{\theta}{2}}, \frac{n_1 - n_2}{2 \sin \frac{\theta}{2}}

(4)

\frac{l_1 - l_2}{2 \cos \frac{\theta}{2}}, \frac{m_1 - m_2}{2 \cos \frac{\theta}{2}}, \frac{n_1 - n_2}{2 \cos \frac{\theta}{2}}