# cross product

## Calculus cross_product

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### Function : cross_product

#### Summary :

The vector calculator allows the calculation of the cross product of two vectors online.

cross_product online

# Definition of the cross product

In an orthonormal coordinate system (O,vec(i),vec(j),vec(k)), the cross product of vectors vec(u)(x,y,z) and vec(v)(x',y',z') has coordinates (yz'-zy',zx'-xz',xy'-yx'), it notes vec(u)^^vec(v).

# Cross product properties

• if vec(u) and vec(v) are collinear then vec(u)^^vec(v)=0
• vec(u)^^vec(v) is orthogonal to vec(u) and vec(v). vec(u),vec(v),vec(u)^^vec(v) form a direct orthogonal reference.

# Calculating the cross product online

The calculation of the cross product of two vectors online is done very quickly, with the cross product calculator, just enter the coordinates of the two vectors and then click the button that allows to perform the calculation of the vector product. To calculate the cross product of the following vectors vec(u) [1;1;1] et vec(v) [5;5;6] , enter the expression cross_product([1;1;1];[5;5;6]) after calculation the résults [1;-1;0] is returned.

The cross product calculator is able to perform calculations by specifying the calculation steps, the vectors can have coordinates also well numeric than literal.

The vector calculator allows the calculation of the cross product of two vectors online.

#### Syntax :

cross_product(vector;vector)

#### Examples :

This example shows how to use the cross product calculator :

cross_product([1;1;1];[5;5;6]), returns [1;-1;0]

Calculate online with cross_product (cross product)