Part of V3D-02 — Three-Dimensional Geometry

Line of Intersection of Two Planes

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To find the line of intersection of planes a1a_{1}x+b1b_{1}y+c1c_{1}z+d1d_{1} = 0 and a2a_{2}x+b2b_{2}y+c2c_{2}z+d2d_{2} = 0: (1) Direction of the line = n1n_{1} x n2n_{2} (cross product of normals). (2) Find any point on both planes (set one variable = 0 and solve the system of two equations in two unknowns). (3) Write the line equation using this point and direction. Alternatively, use the symmetric form directly by expressing two of the three variables in terms of the third.

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