The Vector Cross Product (V x U) computes the resulting vector (W) that is normal to the plane defined by two vectors (V and U) in three dimensional space.
INSTRUCTIONS: Enter the following:
- (V): Enter the x, y and z components of V
- (U): Enter the x, y and z components of U
Vector Cross Product (W): The calculator returns the cross product vector (e.g. 1,-2,1)
The Math / Science
The cross product of two vectors create a third vector that is orthogonal (90 degrees) from both original vectors. This is know as a normal vector to the plane created by vectors U and V. For this reason, a single normal vector is often used to define a plane. To compute the cross product of two vectors, compute the determinant of the following:
| i j k |
V x U = |Vx Vy Vz|
|Ux Uy Uz|
V x U = (Vy⋅ Uz - Uy⋅ Vz), -1(Vx ⋅ Uz - Ux ⋅ Vz), (Vx ⋅ Uy - Ux⋅Vy)
- 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.
- (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