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Cartesian scalar equation of plane

  1. Mar 31, 2010 #1

    yxj

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    Just wanted to confirm. Cartesian scalar equation of plane refers to equation of plane right?
    As in Ax+By+Cz=D. which i think is the vector equation of a plane. I'm getting confused and need clarification
    thank you

    edit= ok sorry.. i think i got it figured out =p scalar is there because.. equation of plane is a dot product. right?
     
    Last edited: Mar 31, 2010
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  3. Mar 31, 2010 #2

    radou

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    Homework Helper

    Last edited by a moderator: Apr 24, 2017
  4. Mar 31, 2010 #3
    The expression

    ax+by+cz+d=0 refers to a plane and is the general scalar Cartesion expression.

    (Aside I wonder if the other expression you were referring to is the direction cosine version

    lx+my+nz+p=0.)

    This in itself is not a vector expression either, but it does lead to the identification of a unique vector, normal to the plane.

    This vector, n = (a,b,c)

    The vector expression for a plane is given by

    [tex]n.(r - {r_0})[/tex]

    edit should read

    [tex]n.(r - {r_0})=0[/tex]

    n intersects the plane at the point [tex]{r_0} = ({x_0},{y_0},{z_0})[/tex]

    r is the position vector [tex]r = (x,y,z)[/tex]


    ax+by+cz
    This part of the equation defines a series of parallel planes all normal to the vector n
    d
    selects the particular plane of interest
     
    Last edited: Mar 31, 2010
  5. Mar 31, 2010 #4

    yxj

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    and cartesian form would be (x,y,z).(#,#,#)=# or Ax+By+Cz=D
     
  6. Mar 31, 2010 #5
    Cartesian refers to rectangular coordinates x,y,z.
    As opposed to some other coordinate system eg r,[tex]\phi[/tex],[tex]\theta[/tex]
     
  7. Mar 31, 2010 #6

    yxj

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    erm.. thah means.. if they were to ask cartesian form of equation of plane should i write
    a) (x,y,z).(A,B,C)=D aka r.(A,B,C,)=D
    b) Ax+By+Cz=D
     
  8. Mar 31, 2010 #7
    I've said it once.

    You can put the d on the other side of the equation if you like, so long as you are careful to get the signs right.


    With regards to your last post


    Both (a) and (b) are cartesian since n and r are cartesian vectors.

    Cartesian refers to the coordinate system, not the vectors or the planes themselves.


    (b) I think (b) is the form you are looking for.

    (a) is not quite correct - the expression should not contain d - this is already included in [tex]{r_0}[/tex] - your expression should equal zero, not =D.

    Sorry I missed the =0 from the vector expression earlier I have amended that post.
     
    Last edited: Mar 31, 2010
  9. Mar 31, 2010 #8

    yxj

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    thank you so much.. it's much clearer now xD
     
  10. Mar 31, 2010 #9
    Glad to help.
     
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