` = "Vector Components 3D"`
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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 `)
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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