How to find out equation of a plane intersecting with other ?

  • Thread starter the_rising
  • Start date
  • Tags
    Plane
In summary, you can find the normal vector of the unknown plane by taking the cross product of the two known planes' normal vectors. The resulting vector will be parallel to the line of intersection. To determine the specific normal vector, you can use the equations n.m = -cos(x) and n.v = 0, where n is the unknown normal vector, m is the normal vector of the known plane, and v is a point on the intersecting line.
  • #1
the_rising
3
0
Hello everyone,
My question is -- Suppose we have two planes intersecting each other in some line. If we know a point on the intersecting line and the normal vector of the one plane and the angle between two planes, can we find out the normal vector of the other plane ?
Please respond.

Regards,
 
Physics news on Phys.org
  • #2
The normal vector of the unknown plane is perpendicular to the line of intersection, so if the line is parallel to the vector v, then n.v = 0, where n is the normal of the unknown plane. If m is the normal vector of the known plane, take m/|m| to ensure you have a vector of length 1. Stipulate that |n| = 1. Then n.m = |n||m|cos(pi - x) = cos(pi - x) = -cos(x), where x is the known angle between planes. You have two important equations:

n.m = -cos(x)
n.v = 0

In fact, you also know that:

v.m = 0

Try to use these.
 
  • #3
mmmmmm...just take the cross product of the 2 normals to get the 3rd normal which will will be parallel to the line of intersection. and depending on what point P0you want it to pass through
N.P-N.P0=0 --> so if n and m are the normals

(nxm).(P-P0)=0 is your solution where P is just variables
 

1. What is the equation of a plane?

The equation of a plane is a mathematical representation of a flat, two-dimensional surface in a three-dimensional space. It is typically written in the form of Ax + By + Cz + D = 0, where A, B, and C are the coefficients of the variables x, y, and z, and D is a constant term.

2. How do you find the equation of a plane given three points?

To find the equation of a plane given three points, you can use the cross product of two vectors formed by the points. First, find two vectors by subtracting one point from the other two. Then, take the cross product of these two vectors to get a normal vector to the plane. Finally, plug in the coordinates of one of the points and the normal vector into the standard form equation (Ax + By + Cz + D = 0) to find the values of A, B, C, and D.

3. What is the difference between a plane and a line?

A plane is a two-dimensional surface that extends infinitely in all directions, while a line is a one-dimensional object that extends infinitely in only one direction. A plane is defined by three non-collinear points, while a line is defined by two points.

4. Can a plane intersect with another plane?

Yes, a plane can intersect with another plane. When two planes intersect, they form a line where all the points of one plane meet with the points of the other plane. This line is called the intersection line and can be found by setting the two plane equations equal to each other and solving for the values of x, y, and z.

5. How do you find the point of intersection between a plane and a line?

To find the point of intersection between a plane and a line, you can substitute the coordinates of the line into the equation of the plane and solve for the remaining variable. This will give you the coordinates of the point where the line intersects the plane.

Similar threads

Replies
26
Views
2K
Replies
4
Views
1K
Replies
1
Views
944
Replies
8
Views
1K
Replies
4
Views
1K
  • Sci-Fi Writing and World Building
Replies
9
Views
2K
  • Calculus
Replies
10
Views
3K
  • Calculus
Replies
3
Views
1K
  • Linear and Abstract Algebra
Replies
10
Views
1K
Replies
36
Views
4K
Back
Top