MHT CET 2020 Math Solved Paper

Any plane through the given line
2x−y+3z+1+λ(x+y+z+3)=0
( From S+λS′=0)
If this plane is parallel to the line ‌

x

1

=‌

y

2

=‌

z

3

,
then the normal to the plane is also perpendicular to the above line.
∴‌‌(2+λ)1+(λ−1)2+(3+λ)3=0
(∵l1l2+m1m2+n1n2=0)
⇒‌‌λ=−‌

3

2

and the required plane is x−5y+3z−7=0.