
Linear Algebra Linear Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
October 3rd, 2015, 01:59 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, 03:43 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 21,105 Thanks: 2324 
L is the plane containing all the lines that are perpendicular bisectors of PQ.

October 13th, 2015, 08:34 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.


Tags 
equation, find, plane, point, points 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Find a fitting plane to given 3d points  maulik13  Applied Math  4  September 20th, 2011 03:03 PM 
Find the Cartesian equation of a plane in R^3  abrahamtim  Linear Algebra  1  May 8th, 2011 10:14 AM 
Points on a plane  wnzguitar  Algebra  2  March 27th, 2011 07:11 AM 
Equation for Plane given 3 points  Anonymouse7  Calculus  1  January 27th, 2010 11:38 AM 
Points in a plane  aman_cc  Applied Math  5  November 21st, 2009 02:06 AM 