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The Vector Components (3D) calculator computes the components of a vector in three dimensions (3D).
INSTRUCTIONS: Enter the following:
- (`vecF`) Vector F
Vector Components: The calculator returns the following:
- |`vecF`| - Magnitude of Vector (Note: Units will be the same as input vector)
- `hatF` - Unit Vector
- (ρ,θ,φ) Spherical Coordinates with θ and φ in degrees (θ°,φ°)
- (r,Θ,z) Cylindrical Coordinates with θ in degrees (θ°)
- α - Angle between `vecF` and x axis
- φ - Angle between `vecF` and y axis
- θ - Angle between `vecF` and z axis
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.
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α = acos( `hatF * 1,0,0 `)
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φ = acos( `hatF * 0,1,0 `)
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θ = acos( `hatF * 0,0,1 `)
3D Vector Functions
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
