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`alpha = "acos"(hatV*hatU)`

Enter a value for all fields

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

**INSTRUCTIONS:** Enter the following:

- (
**V**): Vector V - (
**U**): Vector U

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

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

α = acos(`hatU * hatV`)

where:

- α = angle between `vecV` and `vecU`
- `hatU` = unit vector for `vecU`
- `hatV` = unit vector for `vecV`

- 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.

**k⋅V**- scalar multiplication**V/k**- scalar division**V / |V|**- Computes the**Unit Vector****|V|**- Computes the**magnitude of a vector****U + V**- Vector addition**U - V**- Vector subtraction**|U - V|**- Distance between vector endpoints.**|U + V|**- Magnitude of vector sum.**V • U**- Computes the dot product of two vectors**V x U**- Computes the cross product of two vectors**V x U • W**- Computes the mixed product of three vectors**Vector Angle**- Computes the angle between two vectors**Vector Area**- Computes the area between two vectors**Vector Projection**- Compute the vector projection of V onto U.**Vector Rotation**- Compute the result vector after rotating around an axis.**Vector Components 3D**- Returns a vector's magnitude, unit vector, spherical coordinates, cylindrical coordinates and angle from each axis.**(ρ, θ, φ) to (x,y,z)**- Spherical to Cartesian coordinates**(x,y,z) to (ρ, θ, φ)**- Cartesian to Spherical coordinates**(r, θ, z) to (x,y,z)**- Cylindrical to Cartesian coordinates**(x,y,z) to (r, θ, z)**- Cartesian to Cylindrical coordinates**(x,y) to (r, θ)**- Cartesian to Polar**(r, θ) to (x,y)**- Polar to Cartesian- Vector Normal to a Plane Defined by Three Points