Vectors, Planes, and Spheres, OH MY (Help mep lease)

Click For Summary

Homework Help Overview

The problem involves finding the equation of a plane that contains specific points related to a sphere and is parallel to a given line. The sphere is defined by its equation, and the line is provided in vector form.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the identification of the sphere's center and the "south pole" point. Questions are raised about the necessary components to define the plane, including the directional vector of the line and the method to find a normal vector for the plane.

Discussion Status

Some participants are seeking clarification on the problem's requirements and are encouraging the original poster to share partial attempts. There is a focus on understanding the definitions and relationships between the elements involved in the problem.

Contextual Notes

The original poster expresses frustration about the complexity of their attempts and the need for assistance, indicating a potential lack of confidence in their progress. There is also a suggestion that not all work needs to be shared, which may influence the depth of the discussion.

jdj0202
Messages
3
Reaction score
0

Homework Statement



Find an equation of the plane that contains both the center and "south pole" of the sphere

(x-3)^2+(y-2)^2+(z-3)^2 = 400

and is parallel to the line given in vector form by r(t) = [-43*t-82, -44*t+39, -84*t+94]. Write your answer in the form ax + by + cz = d

Homework Equations


The Attempt at a Solution



All of my attempts are so long it would be absurd to type them up; this is my last ditch effort at finding an answer before giving up.

Please help me with this, thanks.
 
Physics news on Phys.org
If I'm not going to get help because I didn't type up all of my work, will someone let me know so I can put it in here? Thanks.
 
Is my question too hard? If so, I agree.
 
You don't have to put in all of your efforts. Pick one that seems halfway reasonable, and show us what you have tried to do.
 
I will ask you few questions.

Can you determine the center of the sphere with its equation given?

Can you determine the directional vector of the line?

And finally, what is the south pole of the sphere?
 
To find the equation of a plane, you have to find a vector normal to the plane. And that will be the cross product of two vectors in or parallel to the plane. One you are given and the other is the vector from the center of the sphere to it "south pole" (by which I guess you mean the point on the sphere with lowest z).
 

Similar threads

Applying Stokes' Theorem to the part of a Sphere Above a Plane
  • · Replies 21 ·
Replies
21
Views
4K
Vector Equation of Plane w/ (-2,2,1) & Parallels (1,1,2) and (2,1,-1)
  • · Replies 1 ·
Replies
1
Views
1K
Parameterizing Planes Question #2
  • · Replies 6 ·
Replies
6
Views
2K
Analytic geometry: equations of planes (checking answers)
  • · Replies 12 ·
Replies
12
Views
2K
Parametrize plane-sphere intersection
  • · Replies 5 ·
Replies
5
Views
7K
Finding the Equation for a Plane Orthogonal to a Given Line
  • · Replies 11 ·
Replies
11
Views
2K
Intersection Line for Two Planes
  • · Replies 5 ·
Replies
5
Views
2K
How do I find a plane that contains two given lines?
  • · Replies 3 ·
Replies
3
Views
2K
Distance from a point in space to a plane passing through a point
  • · Replies 8 ·
Replies
8
Views
2K
Pick a,b,c,d for y=ax^3+bx^2+cx+d that models path of plane.
  • · Replies 7 ·
Replies
7
Views
2K