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Math Help - intersections

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    intersections

    Suppose P and Q are two distinct planes in R. What sort of set could their intersection be?
    Answer in words and give a sketch to show the possibilities.
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  2. #2
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    Quote Originally Posted by federer View Post
    Suppose P and Q are two distinct planes in R. What sort of set could their intersection be?
    Answer in words and give a sketch to show the possibilities.
    If they are parallel their intersection is the null set.

    If they are not parallel their intersection is a straight line.

    RonL
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  3. #3
    Lord of certain Rings
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    Quote Originally Posted by federer View Post
    Suppose P and Q are two distinct planes in R. What sort of set could their intersection be?
    Answer in words and give a sketch to show the possibilities.
    Another point of view:
    Two planes in R^3, correspond to 2 linear equations in three variables.
    Now what can you tell about the solution to this system.

    Can it have a unique solution?Can it have infinitely many solutions? Can it have no solutions?
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