NDA Math Three Dimensional Geometry

The equation of line through given points is

x−2

−2

=

y−1

3

=

z−3

−2

=k
The equation of plane 2x+y−z=3
⇒−4k+4+3k+1+2k−3=3
⇒k=1
⇒x=0,y=4,z=1
Let the plane divides the line in the ratio r:1
Using section formula for X-coordinate, we get
0=

4r+2

r+1

⇒r=−

1

2

Hence, the plane divides the line externally in the ratio 1:2
So none of the options (a), (b) and (c) is correct.