Calculating the Equation of a Plane Perpendicular to a Given Line

Click For Summary

Homework Help Overview

The discussion revolves around finding the equation of a plane that is perpendicular to a given line and passes through a specific point in three-dimensional space. The subject area involves vector geometry and the properties of planes and lines in 3D space.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to understand how to derive the equation of a plane given a point and a line in a specific vector form. Some participants question whether the direction vector of the line is sufficient to determine the normal vector of the plane. Others explore the relationship between the normal vector and the line's direction.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of how to relate the line's direction to the plane's normal vector. There is a focus on clarifying the geometric relationships involved, but no consensus has been reached yet.

Contextual Notes

Participants note that the examples in the original poster's textbook present the concept differently, which may contribute to the confusion regarding the application of the given vector form.

daynat18
Messages
2
Reaction score
0
Equation for plane that passes through the point (2,-1,3) and is perpendicular to the linev=(1,-2,2)+t(3,-2,4)?

I'm not exactly sure where I'm supposed to go since the only examples in my book show the plane perpendicular to a vector written in a different form. Not in this one
 
Physics news on Phys.org
If a line is given in the form (x0, y0, z0[/sub])+ t(A, B, C) then Ai+ Bj+ Ck is a vector pointing in the direction of the line. Is that enough?
 
So is it supposed to be that I can find the plane based on simply that vector since any of the normal vectors would be orthogonal to the plane?
 
daynat18 said:
So is it supposed to be that I can find the plane based on simply that vector since any of the normal vectors would be orthogonal to the plane?

Well the normal will be perpendicular to the plane, but so is the line v. So wouldn't the normal to the plane be given by the direction of the line v? Given the normal to the plane and a point in the plane, you should be able to calculate the equation of the plane.
 

Similar threads

  • · Replies 23 ·
Replies
23
Views
3K
Replies
6
Views
4K
  • · Replies 3 ·
Replies
3
Views
2K
Replies
1
Views
1K
Replies
1
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 7 ·
Replies
7
Views
3K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 3 ·
Replies
3
Views
3K
  • · Replies 3 ·
Replies
3
Views
2K