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October 3rd, 2015, 01:59 PM   #1
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2 Points in R3 and 1 point on plane. How to find equation of plane?

Let P = (−1, 3, −2) and Q = (1, −1, 4) be points in R3.
Let L be the plane consisting of all the points (x, y, z) such that the distance between (x, y, z) and P is the same as the distance between (x, y, z) and Q.

Using the Euclidean Distance equation between (x,y,z) to P and (x,y,z) to Q and setting these equal to each other I was able to simplify it to what seems like the general equation of a plane.

However I cannot picture geometrically how knowing these two distances results in the equation of a plane.
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October 3rd, 2015, 03:43 PM   #2
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L is the plane containing all the lines that are perpendicular bisectors of PQ.
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October 13th, 2015, 08:34 AM   #3
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If instead P = (0,0,1) and Q=(0,0,-1) then it's pretty easy to visualize the solution as the plane z=0. By some suitable linear coordinate transformation, it's the same picture for general P and Q.
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