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The coplanar points A,B,C,D are (2-x,2,2...

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

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, `vec(AB)=xhati-yhatj`
`vec(AC)=xhati-zhatk`
`vec(AD)=(x-1)hati-hatj-hatk`
As these vectors are coplanar
`|{:(x,,-y,,0),(x,,0,,-z),(x-1,,-1,,-1):}|=0`
`rArr 1/x+1/y+1/z=1`
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