If θ is the angle between two lines whose d.cs are l1 , m1 ,n1 and l2 , m2 ,n2 then the d.cs of one of the angular bisector of the two lines are

Question

If θ is the angle between two lines whose d.cs are l1 , m1 ,n1 and l2 , m2 ,n2 then the d.cs of one of the angular bisector of the two lines are (A) (l2 + l2/2) , (m1 + m2/2) , (n1 + n2/2) (B) (l1 + l2/2 cos ( (θ)2 )) , (m1 + m2/2 cos ( (θ)2 )) , (n1 + n2/2 cos ( (θ)2 )) (C) (l1 + l2/ cos ( (θ)2 )) , (m1 + m2/ cos ( (θ)2 )) , (n1 + n2/ cos ( (θ)2 )) (D) (l1 + l2/2 sin ( (θ)2 )) , (m1 + m2/2 sin ( (θ)2 )) , (n1 + n2/2 sin ( (θ)2 ))

Tardigrade Admin · Accepted Answer

Correct answer is (b) (l1 + l2/2 cos ( (θ)2 )) , (m1 + m2/2 cos ( (θ)2 )) , (n1 + n2/2 cos ( (θ)2 ))

Q. If $θ$ 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

$\frac{l _{2} + l _{2}}{2}, \frac{m _{1} + m _{2}}{2}, \frac{n _{1} + n _{2}}{2}$

$\frac{l _{1} + l _{2}}{2 cos ( \frac{θ}{2} )}, \frac{m _{1} + m _{2}}{2 cos ( \frac{θ}{2} )}, \frac{n _{1} + n _{2}}{2 cos ( \frac{θ}{2} )}$

$\frac{l _{1} + l _{2}}{cos ( \frac{θ}{2} )}, \frac{m _{1} + m _{2}}{cos ( \frac{θ}{2} )}, \frac{n _{1} + n _{2}}{cos ( \frac{θ}{2} )}$

$\frac{l _{1} + l _{2}}{2 s in ( \frac{θ}{2} )}, \frac{m _{1} + m _{2}}{2 s in ( \frac{θ}{2} )}, \frac{n _{1} + n _{2}}{2 s in ( \frac{θ}{2} )}$

Correct answer is (b) $\frac{l _{1} + l _{2}}{2 cos ( \frac{θ}{2} )}, \frac{m _{1} + m _{2}}{2 cos ( \frac{θ}{2} )}, \frac{n _{1} + n _{2}}{2 cos ( \frac{θ}{2} )}$

Q. If θ is the angle between two lines whose d.cs are l1​,m1​,n1​ and l2​,m2​,n2​ then the d.cs of one of the angular bisector of the two lines are

2l2​+l2​​,2m1​+m2​​,2n1​+n2​​

2cos(2θ​)l1​+l2​​,2cos(2θ​)m1​+m2​​,2cos(2θ​)n1​+n2​​

cos(2θ​)l1​+l2​​,cos(2θ​)m1​+m2​​,cos(2θ​)n1​+n2​​

2sin(2θ​)l1​+l2​​,2sin(2θ​)m1​+m2​​,2sin(2θ​)n1​+n2​​