geometry - Describe a plane with z = ax + by + c -
i have 3 points in 3-d space. want describe plane defined these 3 points equation z = ax + + c. how can find values of a, b, , c so?
said way: have plane described equation z = ax + + c. have 2 points want remain in plane, , third point not yet lie in plane. want rotate plane axis described first 2 points, third point in plane, , find a, b, , c describe new plane using same formula. i've looked how rotate point in plane axis (and how find correct angle of rotation given new point want plane pass through), i'm not sure how work ax + + c there.
said yet way (this convenient way me think it): have function f(x,y) = ax + + c, , want change value of f(x1,y1) amount without changing f(x2,y2) or f(x3,y3).
substitute coordinates of points (xi,yi,zi) plane equations, , solve system of linear equations unknown a,b,c. cramer's rule suitable three-unknowns system. if have math library ready-to-use gauss elimination, lu method or solving methods, can use them.
a*x1 + b*y1 + c = z1 a*x2 + b*y2 + c = z2 a*x3 + b*y3 + c = z3 
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