The correct option is B (1,3,4)
The plane x+2y+2z=15 cuts the sphere x2+(y−1)2+(z−2)2=16 in a circle.
The center of the circle is the foot of perpendicular from the center of the sphere to the given plane. Let (p,q,r) be the foot of perpendicular.
p−01=q−12=r−22=−(0+2+4−15)9⇒(p,q,r)=(1,3,4)