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The distance of the point (-1,-5,-10) fr...

The distance of the point `(-1,-5,-10)` from the point of intersection of the line `(x-2)/2=(y+1)/4=(z-2)/12` and the plane `x-y+z=5` is

A

`2sqrt(14)`

B

8

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)=lambda" "["say"]…(i)`
and equation of plane is
`x-y+z=16" "…(ii)`
Any point on the line (i) is, `(3lambda+2,4lambda-1,12lambda+2)`
Let this point of intersection of the line and plane.
`:.(3lambda+2)-(4lambda-1)+(12lambda+2)=16`
`implies" "11lambda+5=16`
`implies" "11lambda=11`
`implies" "lambda=1`
So, the 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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