A variable plane moves so that the sum of the reciprocals of its intercepts on the coordinate axes is `(1//2)`. Then, the plane passes through the point

Options

A. `((1)/(2),(1)/(2),-(1)/(2))`
B. `(-1,1,1)`
C. `(2,2,2)`
D. `(0,0,0)`

Answer

C

Explanation

Let equation of plane be
`(x)/(a)+(y)/(b)+(z)/(c)=1` . . . (i)
Then, according to the given condition
`(1)/(a)+(1)/(b)+(1)/(c)=(1)/(2)` . . . (ii)
From Eqs. (i) and (ii), we get
`x=2,y=2,z=2`
`:." "(x,y,z)-=(2,2,2)`