# Cross Product Calculator

Instructions: Use this online Cross Product Calculator to compute the cross product for two three dimensional vectors $$x$$ and $$y$$. All you have to do is type the data for your vectors $$x$$ and $$y$$, either in comma or space separated format (For example: "2, 3, 4", or "3 4 5").

X data (comma separated)
Y data (comma separated)

## More About the Cross Product Calculator

The cross product is an operation conducted for two three dimensional vectors $$x = (x_1,x_2,x_3)$$ and $$y = (y_1, y_2, y_3)$$, and the result of the operation is a three dimensional vector. The cross product method of calculation is not too complicated and it is actually very mnemonic. The formula for the cross product is shown below:

$x \times y = \left| \begin{matrix}\mathbf{i} & \mathbf{j} & \mathbf{k} \\ {{x}_{1}} & {{x}_{2}} & {{x}_{3}} \\ {{y}_{1}} & {{y}_{2}} & {{y}_{3}} \\ \end{matrix} \right|$

The cross product has a strong geometric motivation. Indeed, the cross product corresponds to a vector with magnitude equal to the area of the parallelogram formed by the vectors $$x$$ and $$y$$, with a direction that is perpendicular to the plane formed by the vectors $$x$$ and $$y$$.

### The cross product and the dot product

A related operation for two vectors is the dot product, although the output of a dot product is a scalar and not a vector.

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