Cross Product Calculator

In mathematics, the cross product or vector product is a binary operation on two vectors in three-dimensional space \mathbb {R} ^{3}, and is denoted by the symbol \times. Wikipedia

Formula
A \times B=\left\| A \right\| \left\| B \right\| \sin \theta n
\left\| A \right\| = length of vector A
\left\| B \right\| = length of vector B
\theta = angle between A and B
n = unit vector perpendicular to the plane containing a and b

 

We can use these properties, along with the cross product of the standard unit vectors, to write the formula for the cross product in terms of components. Since we know that i×i=0=j×j and that i×j=k=−j×i, this quickly simplifies to a×b=(a1b2−a2b1)k=|a1a2b1b2|k.

Vector Cross Product Formula | Examples with Excel Template

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