# 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?
• $a(x-x_0) + b(y-y_0) + c(z-z_0) = 0$
• 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 $(1, 3, 0)$, $(-2, 7, 6)$ and $(1, 0, 1)$.
1. Find the equation of the plane which contains the point $(0, -2, 1)$ and is orthogonal to the line $<1+2t, t, 0>$.
1. Are the Two Planes Parallel, Orthogonal or Neither?
Determine whether the two planes $2x+4y+6z=8$ and $x+2y+3z=1$ are parallel, orthogonal, or neither.
1. Determine whether the two planes $-3x+y+8z=4$ and $2x+6y=1$ are parallel, orthogonal, or neither.
1. Intersection of a Plane and a Line
Determine whether the plane $-3x+5y+z=2$ and line $r(t)=\lt2+3t, -5t, 1-t\gt$ intersect.