Angle Between Planes: Calculating the Angle Between Two 3D Planes

In summary, the angle between two 3D planes is the measure of the deviation or inclination of one plane from another, expressed in degrees. It can be calculated using the dot product formula and has properties such as always being acute or obtuse and being independent of plane position and orientation. It cannot be negative and has real-world applications in engineering, navigation, and computer graphics.
  • #1
phospho
251
0
find the angle between planes:

2x + y + 3z = 5
2x + 3y + z = 7

could someone double check this for me, I got 135.58 while the book got 44.4

thanks :s
 
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  • #2
135.6 and 44.4 add up to 180. Interesting, eh?
 
  • #3
voko said:
135.6 and 44.4 add up to 180. Interesting, eh?

yes I noticed that...
 
  • #4
is one the obtuse angle between the planes and the other the acute?
 
  • #5
Yep.
 

FAQ: Angle Between Planes: Calculating the Angle Between Two 3D Planes

1. What is the angle between two 3D planes?

The angle between two 3D planes is the measure of the deviation or inclination of one plane from another, and it is expressed in degrees. This angle is formed by the intersection of the two planes.

2. How do you calculate the angle between two 3D planes?

To calculate the angle between two 3D planes, you can use the dot product formula, which involves finding the dot product of the normal vectors of the two planes and dividing it by the product of their magnitudes. Then, you can use the inverse cosine function to find the angle in radians, which can be converted to degrees by multiplying by 180 and dividing by pi.

3. What are the properties of the angle between two 3D planes?

The angle between two 3D planes has the following properties:

  • It is always acute or obtuse, never a right angle.
  • It is measured in degrees or radians.
  • It is independent of the position and orientation of the planes.
  • It is the same whether measured from plane A to plane B or from plane B to plane A.

4. Can the angle between two 3D planes be negative?

No, the angle between two 3D planes is always positive. If the planes are facing in opposite directions, the angle will be greater than 90 degrees (acute angle) and less than 180 degrees (obtuse angle).

5. What are some real-world applications of calculating the angle between two 3D planes?

Some common real-world applications include engineering design, such as determining the angle of intersection between two walls or the slope of a roof; navigation, such as finding the angle between two flight paths or two ships at sea; and computer graphics, such as determining the orientation of a 3D object in a virtual environment.

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