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Equation of lines and planes

  1. Sep 25, 2006 #1
    A few Questions:

    a)when finding vector equations (for lines), what do you different when they give you a vector and a line parallel to this vector, and a vector and a line perpendicular to the vector.

    b)concerning planes, can someone briefly explain the normal vector.

    Thanks.
     
  2. jcsd
  3. Sep 25, 2006 #2

    radou

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    I'll try to help with b).

    The easiest way to copletely determine a plane is with one point T1 = (x1, y1, z1) (belonging to the plane) and a vector n which is perpendicular to the plane, which we call the normal vector. Now, let T = (x, y, z) be any point in the plane. Obviously, n must be perpendicular to the vector [tex]\vec{T_{1}T}[/tex], which implies n(r-r1)=0 ...(1), where r1 is the radius vector determined by the point T1, and r the radius vector determined by the point T. Further on, (1) directly implies A(x-x1) + B(y-y1)+ C(z-z1) = 0, where n=Ai+Bj+Ck. This is a general equation of a plane.
     
  4. Sep 25, 2006 #3
    Yeah that explains it, so say they give you a point and a vector parallel to the plane, how would you get the Normal? Would you just cross the vector and the point?
     
  5. Sep 25, 2006 #4

    radou

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    A point and a vector parallel to a plane do not determine a plane. They determine an infinite number of planes.
     
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