Three Dimensional Geometry Part 1

Two points on the line (L say)

x

3

=

y

2

,z=1 are(0,0,1) &(3,2,1)
So dr's of the line is <3,2,0>
Line passing through (1,2,1), parallel to L and coplanar with given plane is

→

r

=

^

i

+2

^

j

+

^

k

+t(3

^

i

+2j), t∈R(−2,0,1) satisfies the line (for t=−1 )
⇒(−2,0,1) lies on given plane.
Answer of the question is (2)
We can check other options by finding eqution of plane
Equation plane : |

x−1	y−2	z−1
1+2	2−0	1−1
2+2	1−0	2−1

|=0
⇒2(x−1)−3(y−2) −5(z−1)=0
⇒2x−3y−5z+9=0