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Distance of the point of intersection of the line `(x-3)/(1)=(y-4)/(2)=(z-5)/(2)and` plane `x+y+z=2` from the point (3,4,5) is

A

0

B

6

C

13

D

7

Text Solution

Verified by Experts

The correct Answer is:
B
Given line is `(x-3)/(1)=(y-4)/(2)=(z-5)/(2)=lamda" "` [say]
`:." "-=(3+lamda,4+2lamda,5+2lamda)` . . . . (i)
If P lies on the plane x+y+z=2, then
`(3+lamda)+(4+2lamda)+(5+2lamda)=2`
`rArr" "lamda=-2`
`:.` From Eq. (i)
`P-=(3-2,4+2(-2),5+2(-2))`
`:." "P-=(1,0,1)`
`:.` If Q `-=` (3,4,5), then
`PQ=sqrt((3-1)^(2)+(4-0)^(2)+(5-1)^(2))=6`
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