Question

If $\theta$ is the angle between two lines whose d.cs are $l_1 , m_1 ,n_1$ and $l_2 , m_2 ,n_2$ then the d.cs of one of the angular bisector of the two lines are

• A. $\frac{l_2 + l_2}{2} , \frac{m_1 + m_2}{2} , \frac{n_1 + n_2}{2}$
• B. $\frac{l_1 + l_2}{2 \, cos \left( \frac{\theta}{2} \right)} , \frac{m_1 + m_2}{2 \, cos \left( \frac{\theta}{2} \right)} , \frac{n_1 + n_2}{2 \, cos \left( \frac{\theta}{2} \right)}$
• C. $\frac{l_1 + l_2}{ cos \left( \frac{\theta}{2} \right)} , \frac{m_1 + m_2}{ cos \left( \frac{\theta}{2} \right)} , \frac{n_1 + n_2}{ cos \left( \frac{\theta}{2} \right)}$
• D. $\frac{l_1 + l_2}{2 \, sin \left( \frac{\theta}{2} \right)} , \frac{m_1 + m_2}{2 \, sin \left( \frac{\theta}{2} \right)} , \frac{n_1 + n_2}{2 \, sin \left( \frac{\theta}{2} \right)}$

Answer 1

Answer: (B)

Correct answer is (b) $\frac{l_1 + l_2}{2 \, cos \left( \frac{\theta}{2} \right)} , \frac{m_1 + m_2}{2 \, cos \left( \frac{\theta}{2} \right)} , \frac{n_1 + n_2}{2 \, cos \left( \frac{\theta}{2} \right)}$