
Geometry Geometry Math Forum 
 LinkBack  Thread Tools  Display Modes 
June 19th, 2017, 11:06 AM  #1 
Senior Member Joined: Nov 2015 From: United States of America Posts: 162 Thanks: 21 Math Focus: Calculus and Physics  Can two different equations define the same plane in space?
Hello all, I have been studying planes, and had a quick question that was on my mind. Can you have two different equations in the form of ax+by+cz=d that represent the same plane in space? For the equation of a plane we need a normal vector and a point on the plane. I suppose the normal vector for two equations that are representing the same plane, would have to be the same? However, the point could be different. Using a different point, would this impact the equation of the plane we are defining in space? After thought (after question more so), given a plane ax+by+cz=d, could you find a point on that plane given the equation that defines the plane? Essentially working backwards to find a point on the plane given the equation? Thanks, Jacob 
June 19th, 2017, 11:46 AM  #2 
Senior Member Joined: Sep 2015 From: Southern California, USA Posts: 1,602 Thanks: 816 
if you have $a x + b y + c z =d$ then $\gamma a x + \gamma b y + \gamma c z = \gamma d,~\forall \gamma \in \mathbb{R}$ represents the same plane. As far as finding a point on the plane simply choose values for $x,~y$ and then $\forall c \neq 0$ $z = \dfrac{d  a x  b y}{c}$ 
June 21st, 2017, 11:33 AM  #3 
Senior Member Joined: Oct 2013 From: New York, USA Posts: 561 Thanks: 79 
Regardless of how many variables there are, an equation can be multiplied by an infinite amount of constants to produce an infinite amount of identical equations.


Tags 
define, equations, plane, space 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Equations of a plane  Techgenius  Geometry  6  June 28th, 2017 09:48 AM 
How are plane waves, pforms, and Maxwell's equations related?  Ganesh Ujwal  Physics  1  January 7th, 2015 04:00 AM 
What do these equations define in geometry?  stamer  Geometry  1  September 27th, 2013 10:26 AM 
Slove parametric equations for a point of a plane  tombfighter  Algebra  2  September 11th, 2008 07:15 PM 
Slove parametric equations for a point of a plane  tombfighter  Abstract Algebra  1  December 31st, 1969 04:00 PM 