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Math Help - Plane and a line

  1. #1
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    Plane and a line

    Let U be a plane given by the point x and the normal vector n.

    Suppose that p(t) = y + Vt be the parametric equation of the line l. Find condition on U and l such that:

    a) U || l
    b) l perpendicular U
    c) l intersects U at a single point, find the point.

    Should I start by finding a line in U? And how do I do it?

    I'm sorry, I'm really lost on this one here, because the professor can't speak any English.
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  2. #2
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    Quote Originally Posted by tttcomrader View Post
    Let U be a plane given by the point x and the normal vector n. Suppose that p(t) = y + Vt be the parametric equation of the line l. Find condition on U and l such that:
    a) U || l
    b) l perpendicular U
    c) l intersects U at a single point, find the point.
    a) n \cdot V = 0, the normal and direction vector are perpendicular.

    b) V = \alpha n, the direction vector is parallel to the normal.

    c) n \cdot V \ne 0\;\& \;p(t) \not\subset U
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  3. #3
    Member Henderson's Avatar
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    Just thought I'd point out that for c), if n \cdot V \ne 0\;, then you already know that  \;p(t) \not\subset U, since the normal vector would be perpendicular to any line in the plane.
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