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The shorteast distance from (1, 1, 1) to...

The shorteast distance from `(1, 1, 1)` to the line of intersection of the pair of planes `xy+yz+zx+y^2=0` is

A

`sqrt(8/3)`

B

`2/sqrt(3)`

C

`1/sqrt(3)`

D

`2/3`

Text Solution

Verified by Experts

The correct Answer is:
A
`xy+yz+y^(2)=0`
`rArr y(x+y)+z(x+y)=0`
`rArr` Line of intersection is `x=-y=z`.
Distance of OP on line having direction ratios 1,-1 is `1/sqrt(3)`.
Then required shortest distance `=sqrt(3-1/3)=sqrt(8/3)`.
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