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Homework Help: Cartesian equation of the plane through the given points

  1. May 14, 2012 #1
    1. The problem statement, all variables and given/known data
    For each part, find the cartesian equation of the plane through the given points.
    (1,0,3), (2,-4,3),(4,-1,2)

    3. The attempt at a solution

    No attempt. Dunno how to do :(
  2. jcsd
  3. May 14, 2012 #2


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    Haven't been paying attention in class?:tongue: Use two pairs of those points to get two vectors in the plane: the vector from [itex](x_0, y_0, z_0)[/itex] to [itex](x_1, y_1, z_1)[/itex] is [itex](x_1- x_0)\vec{i}+ (y_1- y_0)\vec{j}+ (z_1- z_0)\vec{k}[/itex].

    The cross product of two vectors is perpendicular to the two vectors so perpendicular to the plane they lie in.

    The equation of a plane with normal vector [itex]A\vec{i}+ B\vec{j}+ C\vec{k}[/itex] containing point [itex](x_0, y_0, z_0)[/itex] is [itex]A(x- x_0)+ B(y- y_0)+ C(z- z_0)= 0[/itex].
  4. May 14, 2012 #3
    I did listen in class but the lecturer only gave notes to copy during class and there is no example given in the notes so that is why. Anyway, I managed to solved it. Thanks a lot sir.. Really appreciate it :)
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