Let a plane passes through the point P(-1,-1,1) and also passes through a line joinning the points Q(0,1,1) and R(0,0,2). Then the distance of plane from the point (0,0,0) is

Options

A. 3
B. 0
C. `(1)/(sqrt(6))`
D. `(2)/(sqrt(6))`

Answer

D

Explanation

Let the equation of plane passing through the point P(-1,-1,1) is
`a(x+1)+b(y+1)+c(z-1)=0` . . . (i)
which passes through the points Q(0,1,1) and R (0,0,2)
`:." "a+2b+0c=0`
`anda+b+c=0`
`rArr" "(a)/(2-0)=-(b)/(1-0)=(c)/(1-2)`
`rArr" "(a)/(2)=(b)/(-1)=(c)/(-1)`
From Eq. (i), `2(x+1)-1(y+1)-1(z-1)=0`
`rArr" "2x-y-z+2=0`
`:.` Distance of plane from point (0,0,0)
`=(0+0+0+2)/(sqrt(2^(2)+(-1)^(2)+(-1)^(2)))=(2)/(sqrt(6))`