AP EAPCET 04-Jul-2022 Shift 2 Paper

(a) Given, the plane normal to the vector
hat‌n=hat‌i+2‌hat‌j+2‌hat‌k
Let equation of plane
x+2y+2z+d=0
Distance of a plane from the origin is 1∕3.
‌‌ Thus, distance ‌=|‌

ax1+by1+cz1+d

√a2+b2+c2

|
‌⇒‌

1

3

=|‌

0+2⋅0+2⋅0+d

√1+22+22

|
‌⇒1∕3=d∕3⇒d=1
Thus, equation of the plane is x+2y+2z+1=0
Comparing given equation of the plane
‌x+py+qz+r=0
‌∴‌‌p=2,q=2,r=1
‌∴‌‌√p2+q2+r2=√22+22+12
‌⇒‌‌√9=3
‌