- vCalc Catalog Home
- V3 - Angle between vectors

# V3 - Angle between vectors

vCalc Reviewed

Equation / Last modified by AndrewBudd on 2018/10/12 16:00
`alpha = `

The **Angle Between Vectors** calculator computes the angle(**α**) separating two vectors (V and U) * Vectors U and V in three dimensions* in three dimensional space.

**INSTRUCTIONS:** Enter the following:

- (
**V**): Enter the x, y and z components of V separated by commas (e.g. 3,9,1) - (
**U**): Enter the x, y and z components of U separated by commas (e.g. 3,9,1)

**Angle Between Vectors (α): **The calculator returns the angle (α) between the two vectors in degrees. However, this can be automatically converted into other angle units via the pull-down menu.

#### The Math

This formula lets the user enter two three-dimensional vectors (V and U) with X, Y and Z components (Euclidean 3-space vectors)

##### To calculate the angle between two vectors:

- calculate the unit vectors associated with vector V and vector U. To do that,
- compute the magnitude of the vectors and then
- do a scalar multiplication for each of the vectors where the scalar(k) is the inverse of the vector's magnitude.

- calculate the dot product of the unit vectors
- calculate the arc-cosine of that dot product to calculate the angle between the vectors in radians.
- converts radians to degrees.

#### 3D Vector Functions

- multiply a vector by a scalar
- divide a vector by a scalar
- add two vectors
- subtract two vectors
- compute the dot product of two vectors
- compute the cross product of two vectors
- compute the unit vector of a vector
- compute the magnitude of a vector
- project a vector onto another vector
- compute the angle between two vectors
- rotate a vector around an axis
- convert spherical coordinates into a vector
- convert a vector into spherical coordinates

#### References

This equation,

**V3 - Angle between vectors**, is used in 2 calculators.**Calculators**