Consider a set of point R in which is at a distance of 2 units from the line `(x)/(1)= (y-1)/(-1)= (z+2)/(2)` between the planes `x-y+2z=3=0 and x-y+2z-2=0`.A. The volume of the bounded figure by points R and the planes is `(10//3sqrt3)pi` cube units.B. The area of the curved surface formed by the set of points R is `(20 pi //sqrt6)` sq. units.C. The volume of the bounded figure by the set of points R and the planes is `(20pi//sqrt6)` cubic units.D. The area of the curved surface formed by the set of points R is `(10//sqrt3)pi` sq. units.

Consider a set of point R in which is at a distance of 2 units from th

1.	Consider a set of point R in which is at a distance of 2 units from the line `(x)/(1)= (y-1)/(-1)= (z+2)/(2)` between the planes `x-y+2z=3=0 and x-y+2z-2=0`.A. The volume of the bounded figure by points R and the planes is `(10//3sqrt3)pi` cube units.B. The area of the curved surface formed by the set of points R is `(20 pi //sqrt6)` sq. units.C. The volume of the bounded figure by the set of points R and the planes is `(20pi//sqrt6)` cubic units.D. The area of the curved surface formed by the set of points R is `(10//sqrt3)pi` sq. units.
Answer» Correct Answer - b,c Distance between the planes is `h= 5//sqrt6`. Also the figure formed is a cylinder, whose radius is `r=2` units. Hence, the volume of the cylinder is `" "pir^(2)h= pi(2)^(2)(5)/(sqrt6)= (20pi)/(sqrt6)` cubic units. Also the curved surface area is `" "2pirh= 2pi(2)(5)/(sqrt(6))= (20pi)/(sqrt6)`