The Vector Components (3D) calculator computes the components of a vector in three dimensions (3D).
INSTRUCTIONS: Enter the following:
Vector Components: The calculator returns the following:
The Math / Science
To compute the angle between the vector and axes, the unit vector is computed.
`hatF` = `vecF / vecF`
Then compute the dot products between the unit vector `hatF` and the unit vectors for the axes (1,0,0) for x, (0,1,0) for y and (0,0,1) for z. The arccosine of each dot product is the angle between them in radians.

α = acos( `hatF * 1,0,0 `)

φ = acos( `hatF * 0,1,0 `)

θ = acos( `hatF * 0,0,1 `)
 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