(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+2â‹…0+2â‹…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 ‌