3 dimensional cube finding an angle

In summary, to find the angle of intersection of the planes formed by triangles EBC and ECD, you need to find the normal vectors to the planes and use the scalar triple product. Substituting the given values, the angle was found to be 55.24 degrees.
  • #1
Toranc3
189
0

Homework Statement


A cube is positioned with its vertices at the following points:

A=(0,0,0) C=(1,1,0) E=(0,0,1) G=(1,1,1)

B=(1,0,0) D=(0,1,0) F=(1,0,1) H=(0,1,1)

What is the angle of intersection of the planes formed by the triangles EBC and ECD


Homework Equations



AB=ABcosθ

Ab=Absinθ

The Attempt at a Solution




I am stuck on this one. I drew a picture but I can seem to figure anything out. Could somebody give me a hint?
 
Physics news on Phys.org
  • #2
To find the angle, you need to find the normal vectors to the planes.
 
  • #3
hi. you can solve by using scalar triple product * = cross product . = dot product
[(A*B).C] = |A| |B| sin 90 |c| cos(θ) here theta angle made by intersection of planes
if substitute all values you will get angle of intersection of two planes
I got 55.24 degree
 

Related to 3 dimensional cube finding an angle

1. What is a 3 dimensional cube?

A 3 dimensional cube, also known as a "cube" or "hexahedron", is a geometric solid figure with six square faces, twelve edges, and eight vertices. It is often used in mathematics and science to represent three-dimensional space.

2. How do you find the angles of a 3 dimensional cube?

To find the angles of a 3 dimensional cube, you can use the formula "180(n-2)/n" where n is the number of sides or faces of the cube. Since a cube has 6 faces, the formula would be 180(6-2)/6 = 180/3 = 60 degrees. This means that all the angles in a 3 dimensional cube are equal to 60 degrees.

3. Why is finding angles in a 3 dimensional cube important?

Finding angles in a 3 dimensional cube is important because it allows us to understand the geometric properties and relationships of a cube. It also helps us to solve problems and make calculations involving cubes in fields such as mathematics, physics, and engineering.

4. Can you use trigonometry to find angles in a 3 dimensional cube?

Yes, you can use trigonometry to find angles in a 3 dimensional cube. Since a cube is made up of six square faces, you can use the Pythagorean theorem (a² + b² = c²) to find the length of the diagonal of each face. From there, you can use trigonometric ratios such as sine, cosine, and tangent to find the angles of the cube.

5. How does finding angles in a 3 dimensional cube relate to real-world applications?

Finding angles in a 3 dimensional cube has many real-world applications, such as in architecture, engineering, and computer graphics. It allows us to accurately measure and construct three-dimensional structures, design buildings and bridges, and create computer-generated images and animations. It is also used in fields such as astronomy and geology to understand the spatial relationships of objects in three-dimensional space.

Similar threads

  • Linear and Abstract Algebra
Replies
3
Views
1K
  • Precalculus Mathematics Homework Help
Replies
7
Views
1K
  • Calculus and Beyond Homework Help
Replies
5
Views
2K
  • Calculus and Beyond Homework Help
Replies
6
Views
1K
Replies
2
Views
3K
  • Precalculus Mathematics Homework Help
Replies
2
Views
3K
  • Introductory Physics Homework Help
Replies
2
Views
2K
  • Precalculus Mathematics Homework Help
Replies
6
Views
2K
Replies
1
Views
2K
  • Calculus and Beyond Homework Help
Replies
1
Views
3K
Back
Top