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Find the angle between the line (x-2)/(3...

Find the angle between the line `(x-2)/(3)=(y-1)/(-1)=(z-3)/(2)" and the plane "3x+4y+z+5=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.

Text Solution

Verified by Experts

The correct Answer is:
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)`
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