# Vector cross product calculator

Online calculator for calculate the cross product of vectors

## Calculate vector cross product

This function calculates the cross product of two vectors. To perform the calculation, enter the vectors and click the Calculate button. Empty fields are counted as 0.

Cross product calculator

 Vector 1 Vector 2 Result * = Decimal places 0 1 2 3 4 6 8 10

## Description and formula for the Vector cross product

In one in the real coordinate space $$\displaystyle \mathbb {R}^{3}$$ with the standard scalar product and the standard orientation applies to the cross product:

$$\vec{a}\; \times\; \vec{b} = \left[\matrix{a_1\\a_2\\a_3}\right] \times \left[\matrix{b_1\\b_2\\b_3}\right] = \left[ \matrix{a_2b_3-a_3b_2\\a_3b_1-a_1b_3\\a_1b_2-a_2b_1 } \right]$$

Example

$$\vec{a}\; \times\; \vec{b} = \left[\matrix{1\\2\\3}\right] \times \left[\matrix{7\\8\\9}\right] = \left[ \matrix{2\cdot 9 - 3\cdot 8\\3\cdot 7 - 1\cdot 9\\1\cdot 8 - 2\cdot 7 } \right] = \left[ \matrix{-6\\12\\-6} \right]$$