NDA Math Three Dimensional Geometry

LetQ(x1,y1,z1)be the image of the point P.
The direction ratios of PQ are 3,−2,2..(i)
The Equation of line is ‌‌

x+2

3

=‌‌

y−1

−2

=‌‌

z+5

2

=r
Coordinates of any point on the line PQ is 3r−2,−2r+1 and 2r−5
Let Q(3r−2,−2r+1,2r−5) be such a point
Let L be the m is point of PQ,L=(‌‌

3r

2

−2,1−r,r−5)
Since L lies on the plan3x−2y+2z+1=0
So,⇒‌‌

17

2

r−17=0⇒r=2
So,coordinates of Q are=(4,−3,−1)...(ii)
Also the mid point of PQ is L=(‌‌

3×2

2

−2,1−2,2−5)
=(1,−1,−3)...(iii)
⇒PQ=2√17>8