How to find equation for surface of a triangle when vertices are given?
Such as when vertices are $(1,0,0),(0,1,0),(0,0,1)$.
Surface given by $x+y+z=1$.
2026-04-04 19:51:52.1775332312
Surface equation for a triangle when vertices are given
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The set of points of the triangle with given vertices is given by its convex closed hull:
$$T = \{a_1v_1+a_2v_2+a_3v_3|a_1 + a_2 + a_3 = 1, a_1,a_2,a_3 \geq 0\}$$ where $v_1,v_2,v_3$ are the vertices. Notice that this generalizes to more vertices and also works for higher dimensions.