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Math Help - Vectors Problem

  1. #1
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    Vectors Problem




    a) Describe the shape of the intersection of the plane z=-3 and the plane y=z in three-space.

    b) list all the possibilities for the intersection of a line and a plane, and draw an example of each.

    help is much appreciated
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  2. #2
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    Quote Originally Posted by notoriousmc View Post



    a) Describe the shape of the intersection of the plane z=-3 and the plane y=z in three-space.

    b) list all the possibilities for the intersection of a line and a plane, and draw an example of each.

    help is much appreciated
    to a):
    If two planes are not parallel then they will intersect in a straight line.

    The given planes are not parallel therefore you'll get a straight line as the intersection between them:

    P_1: (0,0,1)\cdot (x,y,z) = -3 that means: z = -3<br />
    P_": (0,1,-1) \cdot (x,y,z)=0 that means: y-z=0

    Calculate:

    P_1 \cap P_2 = \left\{\begin{array}{lr}x = &t \\y =& -3+0\cdot t \\z=& -3+0\cdot t\end{array}\right.~\implies~(x,y,z)=(0,-3,-3)+t\cdot(1,0,0)


    to b): Let l denote the line and p the plane then
    1. l\cap p = \{P\}\ if\ l \nparallel p

    2. l\cap p = \emptyset\ if\ l \parallel p

    3. l\cap p = l\ if\ l \in p
    Attached Thumbnails Attached Thumbnails Vectors Problem-schnittger_2planes.png  
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