Find the relation between x,y and z

[utkarshakash]

Homework Statement

The coplanar points A,B,C,D are (2-x, 2,2); (2,2-y,2); (2,2,2-z): (1,1,1)

Homework Equations

The Attempt at a Solution

a(2-x, 2,2) + b(2,2-y,2) + c(2,2,2-z) = (1,1,1)

Equating respective components

ax=by=cz=k

The answer is 1/x + 1/y + 1/z = 1 but in my case it does not satisfy this.

 

[Saitama]

Homework Statement

The coplanar points A,B,C,D are (2-x, 2,2); (2,2-y,2); (2,2,2-z): (1,1,1)

Homework Equations

The Attempt at a Solution

a(2-x, 2,2) + b(2,2-y,2) + c(2,2,2-z) = (1,1,1)

Equating respective components

ax=by=cz=k

The answer is 1/x + 1/y + 1/z = 1 but in my case it does not satisfy this.

Look here: http://mathworld.wolfram.com/Coplanar.html

 

[haruspex]

a(2-x, 2,2) + b(2,2-y,2) + c(2,2,2-z) = (1,1,1)

True, but there is another constraint on a, b, c. If the three vectors on the left are not collinear then with arbitrary a, b and c you could generate any vector in the space, not just those in the desired plane.
If you bring in that extra constraint, the result does follow.