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Homework Help: Vector-Parametric Equation of a Plane

  1. Feb 18, 2010 #1
    1. The problem statement, all variables and given/known data
    Find a vector-parametric equation of a plane that contains the point (4,-2,14) and is parallel to the vectors u=2i-4j+7k and v=3i+5j-2K.

    2. Relevant equations
    Vector Parametric Equation of a Plane: r=a+λu+μv
    (if u and v are two non-parallel vectors in the plane)

    3. The attempt at a solution
    If u and v are parallel to the vector, then wouldn't one of the vectors need to be altered in order for the equation to work? If so, I found the cross product of u and v

    u x v= -27i+25j+22k

    But would that work? I am unsure whether it is necessary to change u and v in the first place, because I don't know if the vectors can't be parallel to each other, the unfound vector, or the plane itself. Does anyone know how this can be found?
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Feb 18, 2010 #2


    Staff: Mentor

    Why would you think this? And what equation are you talking about? You're trying to find the equation of the plane in terms of vectors and a couple of parameters.
    The given vectors are parallel to the plane, but obviously not parallel to each other. That can't happen in R2, where two vectors parallel to a line have to be parallel to each other, but it can happen in R3.

    The cross product of your two given vectors gives a vector that is normal to each of them, and hence, to the plane. If you know a point on a plane and its normal, you can find the equation of the plane, either as standard form (ax + by + cz = d) or in terms of the given point and the two vectors.
  4. Feb 18, 2010 #3


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Doesn't your problem exactly fit the relevant equation you have listed?
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