Enter the normal vectors of the planes or their equations into the calculator to determine the angle between them.

## Angle Between Two Planes Calculation Formula

The following formula is used to calculate the angle between two planes.

cos(θ) = (n1 • n2) / (|n1| |n2|)

Variables:

- θ is the angle between the planes (Degrees)
- n1 and n2 are the normal vectors of the planes
- |n1| and |n2| are the magnitudes of the normal vectors
- • denotes the dot product of the vectors

To calculate the angle between two planes, find the dot product of their normal vectors, divide by the product of the magnitudes of the normal vectors, and take the arccosine of the result.

## What is Angle Between Two Planes Calculation?

Calculating the angle between two planes involves determining the angle formed at the intersection of two planes. This requires understanding the orientation of each plane in 3D space, typically described by their normal vectors or equations. Knowing this angle is essential in various fields such as engineering, physics, and computer graphics where spatial relationships are crucial.

## How to Calculate Angle Between Two Planes?

The following steps outline how to calculate the angle between two planes using the given formula.

- First, identify the normal vectors of the two planes.
- Next, calculate the dot product of the normal vectors.
- Determine the magnitudes of the normal vectors.
- Use the formula: cos(θ) = (n1 • n2) / (|n1| |n2|).
- Finally, calculate the angle by taking the arccosine of the result.
- Check your answer with the calculator above to ensure accuracy.

**Example Problem:**

Use the following variables as an example problem to test your knowledge.

Normal Vector 1: (2, 3, -1)

Normal Vector 2: (1, -4, 2)

## FAQ

**1. What is a normal vector?**

A normal vector is a vector that is perpendicular to a plane. It defines the orientation of the plane in 3D space.

**2. How do you find the normal vector of a plane?**

The normal vector of a plane can be found from the plane’s equation (ax + by + cz + d = 0), where (a, b, c) are the components of the normal vector.

**3. Can this calculator be used for different planes in 3D space?**

Yes, the calculator can be used for any planes in 3D space as long as their normal vectors or equations are known.

**4. Is the calculator accurate?**

The calculator provides an estimate of the angle between two planes based on the inputs provided. For exact figures, it’s best to consult more precise mathematical tools or software.