If `D(x_(1),y_(1),z_(1)), E(x_(2),y_(2),z_(2))` and `F(x_(3),y_(3),z_(3))` are the midpoints of the sides BC, CA and AB respectively of a triangle, find its vertices A, B and C.

Answer

`A=(x_(2)+x_(3)-x_(1),y_(2)+y_(3)-y_(1),z_(2)+z_(3)-z_(1))`
`B=(x_(3)+x_(1)-x_(2),y_(3)+y_(1)-y_(2),z_(3)+z_(1)-z_(2))`
`C=(x_(1)+x_(2)-x_(3),y_(1)+y_(2)-y_(3),z_(1)+z_(2)-z_(3))`