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How to find out equation of a plane intersecting with other ?

  1. Jun 24, 2005 #1
    Hello everyone,
    My question is -- Suppose we have two planes intersecting each other in some line. If we know a point on the intersecting line and the normal vector of the one plane and the angle between two planes, can we find out the normal vector of the other plane ?
    Please respond.

  2. jcsd
  3. Jun 24, 2005 #2


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    The normal vector of the unknown plane is perpendicular to the line of intersection, so if the line is parallel to the vector v, then n.v = 0, where n is the normal of the unknown plane. If m is the normal vector of the known plane, take m/|m| to ensure you have a vector of length 1. Stipulate that |n| = 1. Then n.m = |n||m|cos(pi - x) = cos(pi - x) = -cos(x), where x is the known angle between planes. You have two important equations:

    n.m = -cos(x)
    n.v = 0

    In fact, you also know that:

    v.m = 0

    Try to use these.
  4. Jun 24, 2005 #3
    mmmmmm...just take the cross product of the 2 normals to get the 3rd normal which will will be parallel to the line of intersection. and depending on what point P0you want it to pass through
    N.P-N.P0=0 --> so if n and m are the normals

    (nxm).(P-P0)=0 is your solution where P is just variables
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