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Verify that the the line lies wholly in the plane.

  1. May 19, 2012 #1
    1. Question

    Verify that the line with vector equation r = 2i+4j+k + t(-4i-4j-5k) lies wholly in the plane with equation 3x-2y+4z=2.

    2. The attempt at a solution

    r = (2-4t)i + (4+4t)j + (1-5t)k

    3(2-4t)-2(4+4t)+4(1-5t) = 2
    6-12t-8-8t+4-20t = 2
    t = 0


    If t = 0, doesn't that mean that the line only intersects with the plane at 2i+4j+k? So then the line does not lie wholly on the plane. So there must be something wrong with this question.
     
  2. jcsd
  3. May 19, 2012 #2

    tiny-tim

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    Welcome to PF!

    Hi Alshia! Welcome to PF! :smile:
    No, that should be (4-4t)j :wink:

    (and i think the question should say r = 2i+4j+k + t(4i-4j-5k))
     
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