3-Dimensional planes

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Intros
Lessons
  1. 3-Dimensional Planes Overview:
  2. Equation of a Plane
    • How do we get the formula for the equation?
    • a(xx0)+b(yy0)+c(zz0)=0a(x-x_0) + b(y-y_0) + c(z-z_0) = 0
    • What we need for the formula
  3. Finding a Plane with a Parallel Plane & 1 point
    • Get the Normal Vector
    • Plug into the formula
  4. Finding the Equation of a Plane with 3 points
    • Creating 2 vectors
    • Using the Cross Product = Normal Vector
    • Plug into the formula
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Examples
Lessons
  1. Finding the Equation of a Plane
    Find the equation of the plane which contains the points (1,3,0)(1, 3, 0), (2,7,6)(-2, 7, 6) and (1,0,1)(1, 0, 1).
    1. Find the equation of the plane which contains the point (0,2,1)(0, -2, 1) and is orthogonal to the line <1+2t,t,0><1+2t, t, 0>.
      1. Are the Two Planes Parallel, Orthogonal or Neither?
        Determine whether the two planes 2x+4y+6z=82x+4y+6z=8 and x+2y+3z=1x+2y+3z=1 are parallel, orthogonal, or neither.
        1. Determine whether the two planes 3x+y+8z=4-3x+y+8z=4 and 2x+6y=12x+6y=1 are parallel, orthogonal, or neither.
          1. Intersection of a Plane and a Line
            Determine whether the plane 3x+5y+z=2-3x+5y+z=2 and line r(t)=<2+3t,5t,1t>r(t)=\lt2+3t, -5t, 1-t\gt intersect.