AP EAPCET 24-Aug-2021 Shift 1 Paper

Given, foot of perpendicular drawn from origin to the plane is (2,1,2). ∵ Equation of plane
(r−a).n=0
where, a= Position vector of point on the plane
n= normal vector
Now here, a=PV of A
=2

^

i

+

^

j

+2

^

k

n = OA
= PV of A− PV of O=2

^

i

+

^

j

+2

^

k

∴ Equation of plane is
(r−d)n=0
r.n=a.n ⇒r.(2

^

i

+

^

j

+2

^

k

)=4+1+4
r.(2

^

i

+

^

j

+2

^

k

)=9
In cartesian form, equation of plane is
2x+y+2z=9