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October 3rd, 2015, 12:59 PM  #1 
Newbie Joined: Feb 2014 Posts: 15 Thanks: 0  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. 
October 3rd, 2015, 02:43 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,941 Thanks: 2210 
L is the plane containing all the lines that are perpendicular bisectors of PQ.

October 13th, 2015, 07:34 AM  #3 
Newbie Joined: Sep 2015 From: New york Posts: 17 Thanks: 4 
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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equation, find, plane, point, points 
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