`alpha = "acos"(hatV*hatU)`
Enter a value for all fields
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. However, this can be automatically converted into other angle units via the pull-down menu. Note: degrees are rounded to the nearest 1,000 th.
The Math / Science
lets the user enter two three-dimensional vectors (V and U) with X, Y and Z components ( angle between vectors formula ). Euclidean 3-space vectors
α = acos(`hatU * hatV`)
associated with vector V and vector U. To do that,
calculate the unit vectors
and then magnitude of the vectors do a
for each of the vectors where the scalar(k) is the inverse of the scalar multiplication . vector's magnitude calculate the
of the dot product unit vectors calculate the arc-cosine of that
to calculate the angle between the vectors in radians. dot product 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
(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
Vector Normal to a Plane Defined by Three Points
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