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More old material planes, normal and parallel vectors

  1. Apr 30, 2012 #1
    1. The problem statement, all variables and given/known data

    Consider z = -3x - y + 11

    Find a unit vector perpendicular to the plane, and find a vector parallel to the plane.

    2. Relevant equations

    3. The attempt at a solution


    0 = -3x - y + 11 - z
    -11 = - 3x - y - z

    Perpendicular vector is then:

    -3i -j -k

    And to make that a unit vector, divide it by sqrt(11)


    Here's what I'm not sure of. Can I just pick anything that gives me a dot product of 0 with the above?

    Such that:

    - 3a - b - c = 0?

    Choosing a = -3, b = 5, c = 4,

    A parallel vector to the plane is -3i + 5j + 4k?

    Or is that incorrect?
  2. jcsd
  3. Apr 30, 2012 #2


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    It is all correct.
  4. Apr 30, 2012 #3
    Thank you sir.
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