Enter the x,y, and z values of two vectors into the calculator below to determine the cross product as a new vector.

## Cross Product Formula

The formula for calculating the new new vector of the cross product of two vectors is as follows:

- Where
*θ*is the angle between a and b in the plane containing them. (Always between 0 – 180 degrees) - ‖
**a**‖ and ‖**b**‖ are the magnitudes of vectors a and b - and n is the unit vector perpendicular to a and b

In terms of vector coordinates we can simply the above equation into the following:

a x b = (a2*b3-a3*b2, a3*b1-a1*b3, a1*b2-a2*b1)

Where a and b are vectors with coordinates (a1,a2,a3) and (b1,b2,b3).

The direction of the resulting vector can be determined with the right hand rule.

## Cross Product Definition

A cross product, also known as a vector product, is a mathematical operation in which the result of the cross product between 2 vectors is a new vector that is perpendicular to both vectors. The magnitude of this new vector is equal to the area of a parallelogram with sides of the 2 original vectors.

The cross product is not to be confused with the dot product which is a simpler algebraic operation that returns a single number as opposed to a new vector.

## How to calculate a cross product

The following is an example calculating the cross product of two vectors.

- First, lets gather our two vectors a and b. For this example we will assume vector a has coordinates of (2,3,4) and vector b has coordinates of (3,7,8).
- Next we must use the simplified equation above to calculate the resulting vector coordinates of the cross product.
- Our new vector will be denoted c, so first we will want to find the x coordinate. Through the formula above we find x to be -4.
- Using the same method we then find y and z to be .-4 and 5 respectively.
- Finally we having our new vector from the cross product of a X b of (-4,-4,5)

It’s important to remember that the cross product is anti commutative meaning that the the result of a X b is not the same as b X a. In fact a X b = -b X a.

## FAQ

**What is a cross product?**

A cross product is a vector product that is perpendicular to both of the original vectors and is over the same magnitude.

## Related Terms

cross product |

cross product calculator |

how to calculate cross product |

how to find cross product |

what is cross product |

cross product of two vectors |

scalar triple product |

cross product properties |

cross product matrix |

vector cross product calculator |

matlab cross product |

cross product example |

cross product definition |

cross product 2d |

cross product of 2d vectors |

right hand rule vectors |

triple cross product |

cross product of parallel vectors |

torque cross product |

cross product of perpendicular vectors |

cross product calc |

area of parallelogram cross product |

cross product of two vectors calculator |

cross product determinant |

cross product 3d |

cross product of three vectors |

cross product 3×3 |

cross product in cylindrical coordinates |

cross product sin |

cross product of two vectors formula |

cross multiplication formula |

cross product of sets |

cross product direction |

ijk cross product |

cross product of two vectors in 2d |

cross product in spherical coordinates |

area of triangle cross product |

a cross b cross c |

the cross product |

cross method factoring |

cross product definition math |

matrix cross product calculator |

cross product perpendicular |

cross product calculator 3×3 |

cross product angle |

cross product of 3 vectors |

cross product of orthogonal vectors |

double cross product |

find cross product |

cross product meaning |

cross set |

angular momentum cross product |

cross product of two parallel vectors |

cross product associative |

cross product of two matrices |

cross product calculator 3 vectors |

cross vector calculator |

cross product area |

how to find cross product of two vectors |

what does the cross product represent |

cross product linear algebra |

cross product solver |

cross product two dimensions |

cross product parallel |

define cross product |

vector triple product properties |

cross product of two perpendicular vectors |

cross product 2 dimensions |

cross product of same vector |

angle between two vectors cross product |

cross product math |

cross product parallelogram |

cross product example physics |

vector triple product example |

how to find the cross product of two vectors |

cross product sine formula |

cylindrical cross product |

cross multiplication rule |

what does cross product mean |

cross product with itself |

cross product of i and j |

length of cross product |

vector triple product formula |

cross product of two dimensional vectors |

cross product of two sets |

cross product angle formula |

cross product multiplication |

area of triangle using cross product |

x cross z |

cross product of two vectors example |

cross product of two unit vectors |

find cross product of two vectors |

geometric definition of cross product |

cartesian cross product |

axb vector |

right hand rule for vectors |

vector triple product calculator |

orthogonal cross product |

triple cross product calculator |

cross product polar coordinates |

cross product of two 3d vectors |

cross product of vector with itself |

how to find cross product of vectors |

cross product algebra |

r cross product |

what is a cross product in math |

cross product normal vector |

triple cross product formula |

what is cross product used for |

tensor cross product |

how to calculate cross product of two vectors |

online cross product calculator |

magnitude of cross product calculator |

cross product in r2 |

how to find direction of cross product |

how to calculate the cross product |

i cross i vector |

how to find a cross product |

what is the cross product of two perpendicular vectors |

how to find angle between two vectors using cross product |

what is the cross product used for |

what is the cross product of two parallel vectors |

how to calculate a cross product |

how to find magnitude of cross product |

axb cross product |

cross product of two vectors in 3d |

cross product of two same vectors |

area of parallelogram in vector |

2×2 cross product calculator |

3×3 cross product calculator |

cross product of three vectors example |

cross product calculator with variables |

find cross product calculator |

cross multiplication method formula |

how to find vector cross product |

formula for cross multiplication |

what does cross product mean in math |

how to calculate the cross product of two vectors |

3d vector cross product calculator |

what does cross product of two vectors mean |

how to calculate vector cross product |

what is cross product property |

what is cross product of vectors |

how to compute the cross product |

ijk cross product calculator |

vector cross product ijk |

what is cross product in physics |

define cross product of two vectors |

what is the scalar triple product |

cross product of three vectors calculator |

how to find scalar triple product |

find the cross product calculator |

how to find angle using cross product |

how to get cross product of two vectors |

how to get the cross product of two vectors |

what is the cross product of two unit vectors |

cross product 3×3 matrix calculator |

how to find the direction of cross product |

what is the use of cross product |

how to find vector triple product |