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Homework Help: Need help with Scalar Equations

  1. Mar 27, 2012 #1
    1. The problem statement, all variables and given/known data

    Find the scalar equation of the plane containing the points A(-3, 1, 1) and B(-4, 0, 3) and the vector u = [1, 2, 3].

    2. Relevant equations

    I am at a lost, since I can't tell how to figure out the normal vector. I am supposed to find:
    Ax+By+Cz+D=0, where [A,B,C] is the normal vector.

    3. The attempt at a solution

    I don't know. I can find the scalar equation of three separate points, but I am not sure here. Either I am not thinking about this the right way, or I am honestly lost.
  2. jcsd
  3. Mar 27, 2012 #2
    Well, you have two points given. From that you can get a vector.

    Then you'll have two vectors since one is already given.

    From there how would you get the normal vector?
  4. Mar 27, 2012 #3
    This is what I mean, not thinking. cross product, then I have normal vector, and I have my scalar equation.

    Thanks for that.
  5. Mar 27, 2012 #4
    Just so that I don't have to start a new thread, I wanna ask another question about scalar equations (Cartesian equations):
    How do you find the scalar equation when given the vector equation of a line in 3-space?

    I am given an equation like this:
    [x, y, z] = [3, 1, 5] + s[-2, 3, -1] + t[2, 1, -2]

    I am assuming I set one of the vectors as the origin, subtract it from the other vectors, and find the normal of the resulting vectors?

    I am weak in my understanding of scalar equations and just want to double check to see if I am right.
  6. Mar 27, 2012 #5
    You are already given two vectors there.

    You need to take the cross product of those two, which will give you the normal vector.
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