Equation of plane containing line x−y−1=0 and z−1=0 is (x−y−1)+λ(z−1)=0 ⇒x−y+λz−1−λ=0 ..........(i) Since, this plane is parallel to line
x
2
−
z
3
=1 and y=3
x−1
2
=
y−3
0
=
z
3
..........(ii) ∴2(1)+(0)(−1)+3(λ)=0 ⇒λ=−2∕3 Putting the value of lambda in Eq. (i), we get x−y−