Mathematics

Mathematics

Problem

l1,m1,n1l_1, m_1, n_1 and l2,m2,n2l_2, m_2, n_2 are direction cosines of the two lines inclined to each other at an angle θ\theta , then the direction cosines of the internal bisector of the angle between these lines are a. l1+l22sin⁡θ2,m1+m22sin⁡θ2,n1+n22sin⁡θ2\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}} b. l1+l22cos⁡θ2,m1+m22cos⁡θ2,n1+n22cos⁡θ2\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}} c. l1−l22sin⁡θ2,m1−m22sin⁡θ2,n1−n22sin⁡θ2\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}} d. l1−l22cos⁡θ2,m1−m22cos⁡θ2,n1−n22cos⁡θ2\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}}

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