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Homework Help: Does the line lie in the plane?

  1. Mar 11, 2016 #1
    1. The problem statement, all variables and given/known data
    Does the line through the point P(1, 2, 3) with direction vector d = (1, 2, -3) lie in the plane 2x+y-z=3?

    2. Relevant equations

    3. The attempt at a solution
    From the 2x+y-z i can get the vector (2, 1, -3) and the direction vector, their dot product does not equal zero. So, no it does lie on the plane. Just wondering if my intuition is correct.
  2. jcsd
  3. Mar 11, 2016 #2


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    Science Advisor
    Homework Helper
    Gold Member

    Yes because, as you might have added, ##\langle 2,1,3\rangle## is perpendicular to the plane. Or you might have noticed that P isn't in the plane in the first place.
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