Three Dimensional Geometry

Clearly we can observe from the equations that L1 and L2 pass through (1,0,1)
Vectors in the directions of L1 and L2 are (

^

i

−

^

j

+3

^

k

) and (−3

^

i

−

^

j

+

^

k

) respectively which areequimodular and inclined at an acute angle, so their angle bisector will be along their resultant,which is (−2

^

i

−2

^

j

+4

^

k

). So equation of angle acute angle bisector will be

x−1

1

=

y

1

=

z−1

−2

( Clearly 1=m=1)
∵ Point (α,1,γ) lies on this line, then α=2 and γ=−1