Equations of a plane

  • The equation of a plane is Ax + By + Cz + D = 0 where A,B,C,D ∈ R and A or B or C ≠ 0

  • A plane passing through the  three points A(x1, y1, z1), B(x2, y2, z2) and C(x3, y3, z3) is given by the determinant.

  • The equation of a plane which makes intercept a, b, c on the x, y and z axes respectively is
    x/a + y/b + z/c =1

  • The normal form of the equation of a plane is x cos α + y cos β + z cos γ = p where p is the length of the perpendicular from the origin onto the plane and cos α, cos β and cos γ are the direction cosines of the perpendicular.

  •  The general equation of a plane passing through the line Ax + By + Cz + D = ax + by + cz + d is
    Ax + By + Cz + D + k(ax + by + cz + d) = 0 where k ∈ R



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