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Homework Help: Discrete Math Help Urgent Pls =)

  1. Jan 5, 2005 #1
    How do you find the angle between the co-ordinate axis (i.e. the xz plane) and another plane in general?
     
  2. jcsd
  3. Jan 5, 2005 #2

    learningphysics

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    Angle between two planes is the angle between the normals of the planes.
     
  4. Jan 5, 2005 #3

    HallsofIvy

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    Expanding on what learningphysics said, if one plane is given by Ax+ By+ Cz= D and the other by ax+ by+cz= d, then the normal vectors are Ai+ Bj+ Ck and ai+ bj+ ck respectively. u.v= |u||v|cos(θ) so θ, the angle between the two vectors and the angle between the planes, is given by cos(θ)= u.v/(|u||v|).


    In particular, the xz-plane has normal vector j. If the other plane is given by Ax+By+Cz= D, its normal vector is Ai+Bj+Ck. The dot product of those is simply B so the angle between the planes is given by [itex]cos(\theta)= \frac{B}{\sqrt{A^2+B^2+C^2}}[/itex].
     
    Last edited by a moderator: Jan 5, 2005
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