Let the direction ratios of the plane containing lines
x
3
=
y
4
=
z
2
and
x
4
=
y
2
=
z
3
is <a,b,c> ∴3a+4b+2c=0 4a+2b+3c=0 ∴
a
12−4
=
b
8−9
=
c
6−16
a
8
=
b
−1
=
c
−10
∴ Direction ratio of plane =<−8,1,10> Let the direction ratio of required plane is <l,m,n> Then −8l+m+10n=0 .......(1) and 2l+3m+4n=0 ......... (2) From (1) and (2),
l
−26
=
m
52
=
n
−26
∴ D.R.s are <1,−2,1> ∴ Equation of plane: x−2y+z=0