If

be the vertices of an equilateral triangle

, where

and

respectively, Then equation of plane in which

lies, is

Start: Mid point of

is at origin

and length of side

is

So

and from

we have

how can i solve it after that help me

If by "the plane in which A lies" means the plane containing all possible positions of point A, then it is the perpendicular bisector plane to the line segment BC, and its equation is easily derived from the condition AB=AC, and this yields

Here you can click and rotate to see everything https://www.geogebra.org/m/X7YwcuWQ

Thanks gigelmarga .