Processing...

`W = V x U `

Enter a value for all fields

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**separated by commas (e.g. 2,3,4) - (
**U**): Enter the x, y and z components of**U**separated by commas (e.g. 1,2,3)

**Vector Cross Product (W):** The calculator returns the cross product vector (e.g. 1,-2,1)

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 = |V_{x} V_{y} V_{z}|

|U_{x} U_{y} U_{z}|

V x U = (V_{y}⋅ U_{z} - U_{y}⋅ V_{z}), -1(V_{x} ⋅ U_{z} - U_{x} ⋅ V_{z}), (V_{x} ⋅ U_{y} - U_{x}⋅V_{y})

**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