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Homework Help: Planes. Find the equations of the planes in both cartesian and (vector) form.

  1. Jan 21, 2012 #1
    1. The problem statement, all variables and given/known data

    The plane that passes through the point (1, 6, 4) and contains the line
    x = 1 + 2t; y = 2 - 3t; z = 3 - t where t is an element of R

    2. Relevant equations

    x = 1 + 2t; y = 2 - 3t; z = 3 - t

    3. The attempt at a solution
    Let L be the solution.
    L = (1,6,4) - ?

    t = (x -1)/ 2 = (2-y)/3 = 3-z
  2. jcsd
  3. Jan 21, 2012 #2


    Staff: Mentor

    These equations just represent the line that you are given. Instead of just throwing up a bunch of equations, say something about your thought process in finding the equation of the plane.
  4. Jan 21, 2012 #3
    Well I tried making 2 vectors by using the 3 equations.
    I got
    vector x = t(2,-3,-1) = (1,2,3)

    But the two vectors are meant to be s(0,-4,7) + t(-8,0,25) , where s and t are real numbers.
  5. Jan 21, 2012 #4


    Staff: Mentor

    This doesn't make any sense at all. First off, <1, 2, 3> is a vector from the origin to the point (1, 2, 3) on the line. Second, the vector t<2, -3, -1> = <2t, -3t, -t> is a vector that has the same direction as the line.

    There is no value of t for which t<2, -3, -1> = <1, 2, 3>. For every value of t, these vectors point in different directions.
    Based on what you're showing is the answer, I don't believe that you have provided all of the information for this problem. If you know a point on a plane, and a line that goes through it, that is not enough information to determine the equation of a unique plane.

    What is the complete statement of the problem?
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