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March 30, 2017

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Find the vector and scalar equations of the plane containing the line r=(3,5,1)+t(-2,3,1) and the point (1,2,3)

  • Calculus - ,

    We know one direction vector of the plane is (-2,3,1)
    We have to find another.
    Use the two points (3,5,1) and (1,2,3)
    the vector would be (2,3,-2)
    I will assume you know how to find the cross-product between these two vectors.
    I got (9,2,12)

    So the plane has equation
    9x + 2y + 12z = c
    plug in (1,2,3)
    9 + 4 + 36 = c = 49

    scalar equation is
    9x + 2y + 12z = 49

    vector equation is
    r = (3,5,1) + t(-2,3,1) + s(2,3,-2)

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