Three Dimensional Geometry Part 1

Plane passing through : (2, 1, 0), (4, 1, 1) and (5, 0, 1)
|

x−2	y−1	z
2	0	1
3	−1	1

|=0
⇒x+y−2z=3Let I and F are respectively image and foot of perpendicular of point P in the plane.
eqn of line PI

x−2

1

=

y−1

1

=

z−6

−2

=λ(say)
Let I(λ+2,λ+1,−2λ+6)
⇒F(2+

λ

2

,1+

λ

2

,−λ+6)
F lies in the plane
⇒2+

λ

2

+1+

λ

2

+2λ−12−3=0
⇒λ=4
⇒I(6,5,−2)