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

The corss 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 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 \(y\).

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