Part of V3D-02 — Three-Dimensional Geometry

Equation of a Plane — All Forms

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(1) General form: ax + by + cz + d = 0 (normal is (a,b,c)). (2) Normal form: r.n-hat = p, where p is the perpendicular distance from origin. (3) Intercept form: x/a + y/b + z/c = 1 (intercepts on x, y, z axes are a, b, c). (4) Point-normal form: a(x-x1x_{1}) + b(y-y1y_{1}) + c(z-z1z_{1}) = 0. (5) Three-point form: use the determinant involving the three points. The normal to the plane ax+by+cz+d=0 has DRs (a,b,c).

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