1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Finding cartesian equation of plane from 3 points

  1. Jun 12, 2009 #1
    1. The problem statement, all variables and given/known data

    Find a Cartesian equation of the plane P containing A (2, 0, −3) , B(1, −1, 6) and C(5, 5, 0) , and determine if point D(3, 2, 3) lies on P.

    2. Relevant equations

    vector cross product
    ax + by + cz = 0

    3. The attempt at a solution

    Take the cross product of AB and AC to get normal vector.

    AB = -i -j + 9k
    AC = 31 + 5j + 3k

    I used the determinant method at got:
    AB X AC = -48i + 30j -2k

    Now as A, B and C lie on P, take a point say A(2, 0, -3)

    -48(x - 2) +30(y) -2(z + 3) = 0

    rearranging that gives:

    -48x + 30y -2z = -90

    Then putting in the x, y and z values for D the equation holds.

    The question I have is that the answer for the plane given is:

    24x − 15y + z = 45

    Is there a more common method to follow to get this equation rather than the one I got?
  2. jcsd
  3. Jun 12, 2009 #2


    User Avatar
    Science Advisor
    Homework Helper

    The answer is the same one you got. It's just been divided by (-2). That doesn't change the plane. E.g. the equation 9x=3 has exactly the same solutions as 3x=1, doesn't it?
    Last edited: Jun 12, 2009
  4. Jun 13, 2009 #3
    Yes, but why divide by -2? My question was more, how would they get that answer instead? If I am calculating a different (but equivalent) answer then how?
  5. Jun 13, 2009 #4


    User Avatar
    Science Advisor
    Homework Helper

    Hi username12345! :smile:
    Same reason as why we write 3/2 and not 6/4 or 21/14. :wink:

    (and the minus because it's customary to start with x, so it makes sense for the x coefficient to be positive)
  6. Jun 13, 2009 #5


    User Avatar
    Gold Member

    in other words, you do it in the simplest form, about the minus sign,don’t you think [guys] it’s because the many parts in the equation being negative, so we multiply it by the sign [-]?!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook