Find an Equation of Plane Through P (3,3,1) Perpendicular to Planes

Click For Summary
SUMMARY

The discussion focuses on finding the equation of a plane that passes through the point P (3,3,1) and is perpendicular to the planes defined by the equations x + y = 2z and 2x + z = 10. The normal vector for the first plane is <1,1,-2>, while the normal vector for the second plane is <2,0,1>. To determine the required plane's normal vector, the cross product of these two vectors is utilized, leading to the derivation of the plane's equation using the point-normal form.

PREREQUISITES
  • Understanding of 3D coordinate systems
  • Knowledge of vector operations, specifically cross product
  • Familiarity with the equation of a plane in point-normal form
  • Basic skills in linear algebra
NEXT STEPS
  • Study the properties of normal vectors in 3D geometry
  • Learn how to compute the cross product of vectors
  • Explore the derivation of plane equations from normal vectors
  • Practice solving problems involving multiple planes in 3D space
USEFUL FOR

Students and professionals in mathematics, physics, and engineering who are working with 3D geometry and vector analysis.

Giuseppe
Messages
42
Reaction score
0
Hello, can anyone help me with this problem?

Find an equation of the plane through P (3,3,1) that is perpendicular to the planes x +y = 2z and 2x +z =10

Thanks
 
Physics news on Phys.org
First take the two planes you have. The normal to the first is the vector <1,1,-2>. The normal to the second is <2,0,1>. Since both of these will essentially be parallel to the plane you are looking for, you want to find the vector perpendicular to that plane. In other words, the binormal vector to <1,1,-2> and <2,0,1>. How do you do that in a 3 dimensional coordinate system? Try using the cross product, and assuming you know how to get the equation of a plane from the normal vector and a point, you shouldn't have any trouble arriving at an answer.
 

Similar threads

Undergrad Finding vertex of a 3D Triangle on a Plane
  • · Replies 3 ·
Replies
3
Views
2K
MHB How to know if plane is perpendicular to another plane?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Triple equation for integral on a graph
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad Closest point on a plane to a point near the plane
  • · Replies 6 ·
Replies
6
Views
3K
High School How to draw a plane intersecting a cylinder at a "compound angle"
  • · Replies 8 ·
Replies
8
Views
3K
Undergrad Chain Rule (partial derivatives): basic interpretation question
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad 3-parameter group of symmetries on the plane
  • · Replies 51 ·
2
Replies
51
Views
6K
Graduate Projection of 3D Plane from a certain perspective on the 2D Plane
  • · Replies 2 ·
Replies
2
Views
4K
MHB Find Vector Perpendicular to Plane
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Given a vector, how to compute orthogonal plane
  • · Replies 4 ·
Replies
4
Views
3K