How do you find the "z" graph of a tetrahedron when you are only given the vertices?
For example....
What's the "z" graph of a tetrahedron when the xy-plane vertices are (0,2), (0,0), and (1,0) and when z=3 as long as x=0 and y=0?
How do you find the "z" graph of a tetrahedron when you are only given the vertices?
For example....
What's the "z" graph of a tetrahedron when the xy-plane vertices are (0,2), (0,0), and (1,0) and when z=3 as long as x=0 and y=0?
Ok no problem! Then a brief explanation
You gave some points in the space, and . it's possible to form vectors by substracting the coordinates of two given points, with three points we form the vectors and As those vectors are the sides of tetrahedron, they sall belong to the plane we are looking for
From cross product theory, the vector its perpendicular to both , and , that's it, to the plane that belong to those vectors.
Now from dot product theory, if we take some vector with coordinates wich has its end (thinking in vectors as oriented segments) in the point and another vector wich is perpendicular to the plane, the dot product is zero. Explicitly: . Then we have . Our is so this is were my equation comes from.
You're saying that there's something wrong, so there should be some fail in derivation or computation, but at least we're trying!