Question

The direction cosines of the lines bisecting the internal angle $\theta$ between the lines whose direction cosines are $l_1,m_1,n_1$ and $l_2,m_2,n_2$ are

• A. $<l_1+l_2,m_1+m_2,n_1+n_2>$
• B. $<\frac{l_1+l_2}{2\sin \frac{\theta }{2}},\frac{m_1+m_2}{2\sin \frac{\theta }{2}},\frac{n_1+n_2}{2\sin \frac{\theta }{2}}>$
• C. $<\frac{l_1+l_2}{2\cos \frac{\theta }{2}},\frac{m_1+m_2}{2\cos \frac{\theta }{2}},\frac{n_1+n_2}{2\cos \frac{\theta }{2}}>$
• D. none of these

Answer 1

Answer: (C)

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

The direction cosines of the lines bisecting the internal angle $\theta$ between the lines

direction cosines are $l_1,m_1,n_1$ and $l_2,m_2,n_2$ are

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

Option C is correct answer