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The points A(2-x,2,2), B(2,2-y,2), C(2,2...

The points `A(2-x,2,2), B(2,2-y,2), C(2,2,2-z)` and `D(1,1,1)` are coplanar, then locus of `P(x,y,z)` is

A

`(1)/(x)+(1)/(y)+(1)/(z)=1`

B

`x+y+z=1`

C

`(1)/(1-x)+(1)/(1-y)+(1)/(1-z)=1`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
Here, `AB=xhati-yhatj`
`AC=xhati-zhatk,AD=(x-1)hati-hatj-hatk`
As, these vectors are coplanar
`implies|(x-y,0),(x,0,-z),(x-1,-1,-1)|=0implies(1)/(x)+(1)/(y)+(1)/(z)=1`
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