Question

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

Answer 1

Correct Answer - A
We have
`vec(AB)=xhati-yhatj,vec(AC)=xhati-zhatk,vec(AD)=(x-1)hati-hatj-hatk`
Clearly these vectors are coplanar.
`:.|(x,-y,0),(x,0,-z),(x-1,-1,-1)|=0implies1/x+1/y+1/z=1`