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`m = vecV"x"vecU • vecW`
Enter a value for all fields
The vector Mixed Product (V x U • W) calculator computes the dot product of a vector (W) and the cross product of two other vectors (V and U) 
in three dimensional space.
INSTRUCTIONS: Enter the following:
- (V): Vector V
- (U): Vector U
- (W): Vector W
Mixed Product (m): The calculator returns the mixed product as a real number.
The Math / Science
The Mixed Product of three vectors is the cross product of two vectors creating a third vector that is orthogonal (90 degrees) from both original vectors and then the dot product of the result vector and a third vector.
The process is as follows:
- V x U :Cross Product of vectors V and U
- V x U • W : Dot product of vectors VxU and W
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