How to get the equation of the plane. [read this one]

  • Thread starter Thread starter UNIQNESS
  • Start date Start date
  • Tags Tags
    Plane
Click For Summary
SUMMARY

The equation of the plane can be derived from its vertices using the standard form ax + by + cz = 0. By substituting the points (1,1,0) and (0,1,1) into the equation, it is established that a = -b and b = -c. This leads to the simplified equation x - y + z = 0, confirming the relationship between the coefficients and the vertices provided.

PREREQUISITES
  • Understanding of linear algebra concepts, particularly planes in three-dimensional space.
  • Familiarity with the standard equation of a plane: ax + by + cz = 0.
  • Basic skills in substituting coordinates into equations.
  • Knowledge of geometric interpretations of points and planes.
NEXT STEPS
  • Study the derivation of plane equations from points in three-dimensional geometry.
  • Learn about the geometric interpretation of linear equations in 3D space.
  • Explore the use of vector equations for planes and their applications.
  • Investigate the implications of changing coefficients in the plane equation.
USEFUL FOR

Students of mathematics, particularly those studying geometry and linear algebra, as well as educators looking to explain the concept of planes in three-dimensional space.

UNIQNESS
Messages
18
Reaction score
0
http://www.isquaredonline.com/chips/1.jpg

the above link is the answer to the problem I'm solving. i was wondering how i'd come up with the equation of the plane "x-y+z=0" when only the vertices of the plane are provided in the problem. thanks in advance.
 
Last edited by a moderator:
Physics news on Phys.org
The equation of a plane through the origin is always of the form ax+by+cz=0.
Now you can plug in some points. Say, put in (1,1,0) and you'll find a=-b.
Putting in (0,1,1) b=-c. So the equation reduces to ax-ay+az=0 or x-y+z=0.
 
thanks for the help.
 

Similar threads

How does metal sphere determine the potential of the plane by symmetry?
  • · Replies 15 ·
Replies
15
Views
2K
D'Alembert's principle on inclined plane problem
  • · Replies 8 ·
Replies
8
Views
2K
Projectile motion on an inclined plane
  • · Replies 7 ·
Replies
7
Views
2K
Interference pattern of a fan of plane waves
  • · Replies 2 ·
Replies
2
Views
2K
Magnitude and average value of energy intensity of light beam
  • · Replies 10 ·
Replies
10
Views
2K
Is the Block Moving Horizontally or Perpendicularly on the Inclined Plane?
  • · Replies 3 ·
Replies
3
Views
3K
Projectile launched from an inclined plane strikes a wall horizontally
  • · Replies 7 ·
Replies
7
Views
2K
3D Statics problem: Box on an inclined plane constrained by a rope
  • · Replies 19 ·
Replies
19
Views
3K
Path/time function of a freesbie (the ride at amusement parks)
  • · Replies 40 ·
2
Replies
40
Views
3K
Block and pulley on movable incline
  • · Replies 2 ·
Replies
2
Views
2K