Intersection of plane in spherical coordinate system

In summary, the intersection of a plane in spherical coordinate system is the point where the plane intersects the sphere, represented by three coordinates. To find this intersection, the equations of the plane and sphere can be set equal to each other and solved for the unknown variables. It is possible for the intersection to be a circle, and it has significance in mathematics, physics, and engineering. Additionally, the intersection can be used to define a point on a 3D coordinate system.
  • #1
foruforewer
2
0
Dear Friends,

I have below query

Available data:
Point1 (r1,theta1,phi1)
Point2 (r2,theta2,phi2)
where in spherical coordinate system
r(i)=radius
theta(i)=angle
phi(i)=azimuth

Required output:
Line of intersection by individual planes generated by each point i.e. from point1 we got plane1 and from point2 we got plane2.

And azimuth or say angle with 0° of this line.

Please help me in this.
 
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  • #2
Please help me in this
 

1. What is the intersection of a plane in spherical coordinate system?

The intersection of a plane in spherical coordinate system is the point where the plane intersects the sphere. This point is represented by three coordinates - the radius (r), inclination angle (θ), and azimuth angle (φ).

2. How do you find the intersection of a plane and a sphere in spherical coordinate system?

To find the intersection of a plane and a sphere in spherical coordinate system, you can use the equation of the plane and the equation of the sphere. Set the two equations equal to each other and solve for the unknown variables. The resulting values will give you the coordinates of the intersection point.

3. Can the intersection of a plane and a sphere be a circle?

Yes, the intersection of a plane and a sphere can be a circle. This happens when the plane is perpendicular to the center of the sphere and passes through its equator.

4. What is the significance of the intersection of a plane and a sphere in spherical coordinate system?

The intersection of a plane and a sphere in spherical coordinate system is significant in various fields such as mathematics, physics, and engineering. It is used to solve problems related to finding the distance between two points on a sphere, calculating the area of a spherical triangle, and determining the position of objects in spherical coordinates.

5. Can the intersection of a plane and a sphere be used to define a point on a 3D coordinate system?

Yes, the intersection of a plane and a sphere can be used to define a point on a 3D coordinate system. The three coordinates of the intersection point - radius (r), inclination angle (θ), and azimuth angle (φ) - represent the position of the point in the spherical coordinate system.

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