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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