Mathematical Calculators

Vector Cross Product Calculator

Vector cross product calculator finds the cross product of two vectors in a three-dimensional space.

Vector A

Vector B

Vector C = A × B

Table of contents

What is cross product?
Cross Product Calculation Formula
Definition of Cross Product
How to calculate cross product of two vectors
What cross product is?
To determine the cross product of a new vector, you need to enter the x, y, and z values of two vectors into the calculator.

What is cross product?

Cross product is a mathematical operation that takes two vectors and produces a new vector. It is used in many fields, including engineering, physics and mathematics. In this blog post, we’re going to explore what cross product is and what it can do for us. We’ll also give an example of how it’s used in physics. So read on to learn more!

Cross Product Calculation Formula

The formula for calculating the new vector of the cross product of two vectors is the following:
Where θ is the angle between a and b in the plane containing them. (Always between 0 – 180 degrees)
‖a‖ and ‖b‖ are the magnitudes of vectors a and b
and n is the unit vector perpendicular to a and b
In terms of vector coordinates we can simplify the above equation into the following:
a x b = (a2*b3-a3*b2, a3*b1-a1*b3, a1*b2-a2*b1)
Where a and b are vectors with coordinates (a1,a2,a3) and (b1,b2,b3).
The direction of the resulting vector can be determined with the right-hand rule.

Definition of Cross Product

A cross product, which is also known as a vector product, is a mathematical operation. In cross product operation the result of the product between 2 vectors is a new vector that is perpendicular to both vectors. The magnitude of this new vector is equal to the area of a parallelogram with sides of the 2 original vectors.
The cross product should not to be confused with the dot product. The dot product is a simpler algebraic operation that returns a single number as opposed to a new vector.

How to calculate cross product of two vectors

Here is an example of calculating the cross-product for two vectors.
First thing is to gather two vectors: vector A and vector B. For this example, we will assume vector A has coordinates of (2, 3, 4) and vector B has coordinates of (3, 7, 8).
After this we use the simplified equation above to calculate the resulting vector coordinates of the product.
Our new vector will be denoted as C, so first, we will want to find the X coordinate. Through the formula above we find X to be -4.
Using the same method we then find y and z to be .-4 and 5 respectively.
Finally, we having our new vector from the cross product of an X b of (-4,-4,5)
It’s important to remember that the cross product is anti-commutative meaning that the result of a X b is not the same as b X a. In fact:
a X b = -b X a.

What cross product is?

A cross product is a vector product that is perpendicular to both of the original vectors and is over the same magnitude.

John Cruz
Article author
John Cruz
John is a PhD student with a passion to mathematics and education. In his freetime John likes to go hiking and bicycling.

Vector Cross Product Calculator English
Published: Sun Jul 04 2021
In category Mathematical calculators
Add Vector Cross Product Calculator to your own website

Other mathematical calculators

30 60 90 Triangle Calculator

Expected Value Calculator

Online Scientific Calculator

Standard Deviation Calculator

Percentage Calculator

Fractions Calculator

Pounds To Cups Converter: Flour, Sugar, Milk..

Circle Circumference Calculator

Double Angle Formula Calculator

Mathematical Root Calculator (square Root Calculator)

Triangle Area Calculator

Coterminal Angle Calculator

Dot Product Calculator

Midpoint Calculator

Significant Figures Converter (Sig Figs Calculator)

Arc Length Calculator For Circle

Point Estimate Calculator

Percentage Increase Calculator

Percentage Difference Calculator

Linear Interpolation Calculator

QR Decomposition Calculator

Matrix Transpose Calculator

Triangle Hypotenuse Calculator

Trigonometry Calculator

Right Triangle Side And Angle Calculator (triangle Calculator)

45 45 90 Triangle Calculator (right Triangle Calculator)

Matrix Multiply Calculator

Average Calculator

Random Number Generator

Margin Of Error Calculator

Angle Between Two Vectors Calculator

LCM Calculator - Least Common Multiple Calculator

Square Footage Calculator

Exponent Calculator (power Calculator)

Math Remainder Calculator

Rule Of Three Calculator - Direct Proportion

Quadratic Formula Calculator

Sum Calculator

Perimeter Calculator

Z Score Calculator (z Value)

Fibonacci Calculator

Capsule Volume Calculator

Pyramid Volume Calculator

Triangular Prism Volume Calculator

Rectangle Volume Calculator

Cone Volume Calculator

Cube Volume Calculator

Cylinder Volume Calculator

Scale Factor Dilation Calculator

Shannon Diversity Index Calculator

Bayes Theorem Calculator

Antilogarithm Calculator

Eˣ Calculator

Prime Number Calculator

Exponential Growth Calculator

Sample Size Calculator

Inverse Logarithm (log) Calculator

Poisson Distribution Calculator

Multiplicative Inverse Calculator

Marks Percentage Calculator

Ratio Calculator

Empirical Rule Calculator


Sphere Volume Calculator

NPV Calculator

Percentage Decrease

Area Calculator

Probability Calculator