# Plane

Move the blue point and the red point. A red vector is drawn from the blue point to the red point. GeoGebra will draw a teal plane going through the blue point and perpendicular to the red vector. (So, the red vector is a normal vector to the plane.)
In addition, there is a green point labeled (x,y,z) which you can move to be anywhere on the plane. A green vector is drawn from the blue point to the green point. What do you notice about the angle between the red vector and the green vector?
Make an expression to represent the components of the green vector in terms of (x,y,z) and the coordinates of the blue point. Say that red normal vector is <n_1,n_2,n_3>. Based on the angle and the previous explorations, how can you create an equation to describe the plane?

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