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The distance of the point (1, 0, 2) fr...

The distance of the point (1, 0, 2) from the point of intersection of the line `(x-2)/3=(y+1)/4=(z-2)/(12)` and the plane x y + z = 16, is :

A

`2sqrt(14)`

B

3

C

`3sqrt(21)`

D

13

Text Solution

Verified by Experts

The correct Answer is:
D
Given equation of line is
`(x-2)/(3)=(y+1)/(4)=(z-2)/(12)=lamda" "` [say] . . . (i) and equation of plane is
x-y+z+16 . . .(ii)
Let point on the line (i) is `(3lamda+2,4lamda-1,12lamda+2)`.
Let this point be point of intersection of the line and plane.
`:.(3lamda+2)-(4lamda-1)+(12lamda+2)=16`
`rArr" "11lamda+5=16rArr11lamda=11lamda=1`
`:.` Point of intersection is (5,3,14).
Now, distance between the points (1,0,2) and (5,3,14)
`=sqrt((5-1)^(2)+(3-0)^(2)+(14-2)^(2))`
`=sqrt(16+9+144)=sqrt(169)=13`
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