Online calculator. Cross product of two vectors (vector product)

This free online calculator help you to find cross product of two vectors.

Using this online calculator, you will receive a detailed step-by-step solution to your problem, which will help you understand the algorithm how to find cross product of two vectors.

Calculator

Guide

Some theory

Cross product calculator

Form of first vector representation:
Form of second vector representation:

Input vectors:

First vector

= {,

,

}

Second vector

= {,

,

}

a × b

Guide - Cross product calculator

To find the cross product of two vectors:

Select the vectors form of representation;

Type the coordinates of the vectors;

Press the button "=" and you will have a detailed step-by-step solution.

Entering data into the cross product calculator

You can input only integer numbers or fractions in this online calculator. More in-depth information read at these rules.

Additional features of the cross product calculator

You can navigate between the input fields by pressing the keys "left" and "right" on the keyboard.

Theory. Cross product of two vectors

Definition

Cross product (vector product) of two vectors a = {a_{x} ; a_{y} ; a_{z}} and b = {b_{x} ; b_{y} ; b_{z}} in Cartesian coordinate system is a vector defined by:

a × b =

i

j

k

= i (a_{y}b_{z} - a_{z}b_{y}) - j (a_{x}b_{z} - a_{z}b_{x}) + k (a_{x}b_{y} - a_{y}b_{x})

a_{x}

a_{y}

a_{z}

b_{x}

b_{y}

b_{z}

or

a × b = {a_{y}b_{z} - a_{z}b_{y} ; a_{z}b_{x} - a_{x}b_{z} ; a_{x}b_{y} - a_{y}b_{x}}.

The cross product of two vectors a and b is a vector c, length (magnitude) of which numerically equals the area of the parallelogram based on vectors a and b as sides.

The vector product of a and b is always perpendicular to both a and b.