If \[{{l}_{1}},{{m}_{1}},{{n}_{1}}\] and \[{{l}_{2}},{{m}_{2}},{{n}_{2}}\] are direction consines of the two lines inclined to each other at an angle \[\theta \], the direction cosines of the bisector of the angle between these lines are

\[\frac{{{l}_{1}}-{{l}_{2}}}{2\cos \frac{\theta }{2}},\frac{{{m}_{1}}-{{m}_{2}}}{2\cos \frac{\theta }{2}},\frac{{{n}_{1}}-{{n}_{2}}}{2\cos \frac{\theta }{2}}\]

\[\frac{{{l}_{1}}-{{l}_{2}}}{2\sin \frac{\theta }{2}},\frac{{{m}_{1}}-{{m}_{2}}}{2\sin \frac{\theta }{2}},\frac{{{n}_{1}}-{{n}_{2}}}{2\sin \frac{\theta }{2}}\]

If \[{{l}_{1}},{{m}_{1}},{{n}_{1}}\] and \[{{l}_{2}},{{m}_{2}},{{n}_{2

1.	If \[{{l}_{1}},{{m}_{1}},{{n}_{1}}\] and \[{{l}_{2}},{{m}_{2}},{{n}_{2}}\] are direction consines of the two lines inclined to each other at an angle \[\theta \], the direction cosines of the bisector of the angle between these lines are
A.	\[\frac{{{l}_{1}}-{{l}_{2}}}{2\sin \frac{\theta }{2}},\frac{{{m}_{1}}-{{m}_{2}}}{2\sin \frac{\theta }{2}},\frac{{{n}_{1}}-{{n}_{2}}}{2\sin \frac{\theta }{2}}\]
B.	\[\frac{{{l}_{1}}-{{l}_{2}}}{2\cos \frac{\theta }{2}},\frac{{{m}_{1}}-{{m}_{2}}}{2\cos \frac{\theta }{2}},\frac{{{n}_{1}}-{{n}_{2}}}{2\cos \frac{\theta }{2}}\]
C.	\[\frac{{{l}_{1}}-{{l}_{2}}}{2\sin \frac{\theta }{2}},\frac{{{m}_{1}}-{{m}_{2}}}{2\sin \frac{\theta }{2}},\frac{{{n}_{1}}-{{n}_{2}}}{2\sin \frac{\theta }{2}}\]
D.	\[\frac{{{l}_{1}}-{{l}_{2}}}{2\cos \frac{\theta }{2}},\frac{{{m}_{1}}-{{m}_{2}}}{2\cos \frac{\theta }{2}},\frac{{{n}_{1}}-{{n}_{2}}}{2\cos \frac{\theta }{2}}\]
Answer» D. \[\frac{{{l}_{1}}-{{l}_{2}}}{2\cos \frac{\theta }{2}},\frac{{{m}_{1}}-{{m}_{2}}}{2\cos \frac{\theta }{2}},\frac{{{n}_{1}}-{{n}_{2}}}{2\cos \frac{\theta }{2}}\]

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If \[{{l}_{1}},{{m}_{1}},{{n}_{1}}\] and \[{{l}_{2}},{{m}_{2}},{{n}_{2}}\] are direction consines of the two lines inclined to each other at an angle \[\theta \], the direction cosines of the bisector of the angle between these lines are

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