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

Cross product calculator

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

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.

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]