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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 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

**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