# Cross Product Calculator

## Introduction to Cross Product Calculator

The vector product calculator is an online tool to calculate the cross-product of two vectors to multiply them. It uses the expansion method to find the vector product of two vectors and plots a 3D diagram with respect to the given vectors. The cross product is sometimes also known as the vector product.

In vector calculus, scalar and vector are the basic concepts. You often need to find the resultant of two vectors by multiplying them together. The process of finding the resultant of two vectors will be easier using a tool. So that’s why we introduce a tool that can easily evaluate the cross product of two vectors.

## Formula used by Cross Product Vectors Calculator

The vector calculator uses the following formulas to evaluate two given vectors:

The vector product of two vectors A and B in three dimension can be written as:

$$\vec A \;X\; \vec B \;=\; |A||B|sinθ$$

Where

$$\vec A \;=\; (a_1 ,\; a_2 ,\; a_3)$$ $$\vec B \;=\; (b_1 ,\; b_2 ,\; b_3)$$

A×B is the perpendicular vector to both vectors A and B and normal to the plane containing them.

$$The\; normalized\; vector\; of\; the\; product\; \vec C \;=\; \vec A \vec B \; can\; be\; found\; by\; using\; the\; following\; formula:$$ $$\hat C \;=\; ( \frac{c_1}{|C|} \;,\; \frac{c_2}{|C|} \;,\; \frac{c_3}{|C|})$$

Where

$$|C| \;=\; \sqrt{(c_1)^2 \;+\; (c_2)^2 \;+\; (c_3)^2}$$ Example

Consider two vectors A and B can be written as:

A = 2i + 3j - k

B = i - 3j - 2k

We have to find the cross product of these vectors.

Now,

A × B = |i j k 2 3 -11 -3 -2|

A × B = |3 -1 -3 -2|i - |2 -11 -2|j + |2 3 1 -3 |k

A × B = (-6 -3)i-(-4+1)j+(-6-3)k

A × B = -9i + 3j - 9k = C

Now we will find the normal vector of C.

$$\hat C \;=\; \frac{C}{|C|}$$ $$|C| \;=\; \sqrt{(-9)^2 \;+\; (3)^2 \;+\; (-9)^2}$$ $$|C| \;=\; \sqrt{171} \;=\; 3 \sqrt{19}$$

Now the normal vector will be,

$$\hat C \;=\; (\frac{-3}{\sqrt{19}} \;,\; \frac{1}{\sqrt{19}} \;,\; \frac{-3}{\sqrt{19}})$$

## How to find cross product of 2 vectors

There are some steps to using this tool. These are:

1. Search the website calculatores.com from your desired browser. And select the vector cross product calculator from the list of available tools.
2. In the first step, enter the values for vector A in the X, Y, and Z boxes.
3. Now enter the values of vector B in the X, Y, and Z boxes.
4. Click on the “Calculate” button.

After a few seconds of clicking on the calculate button, you will get the results.

## Why to use Cross Product 2 Vectors Calculator?

In mathematics and physics, vectors and scalars are important to describe the magnitude and the direction of different quantities. We usually do this for 2 vectors. So the product calculator can be used to find the cross product and the normalized vector for it.

When calculating the cross product, sometimes you forget the formula, or you may skip a term to expand. Or sometimes, you may take a lot of time to compute the product because manual calculations may be tricky. That’s why you need this tool to find the cross product of 2 vectors.

## Benefits of using Cross Product 2×2 Calculator

The cross product is referred to as the vector product. It represents the area of a parallelogram whose sides are defined by the two vectors. It also has many applications in real life. So the vector calculator makes it more helpful to find the resultant.

There are some beneficial uses of this tool. These are:

1. It saves your time from manual calculations, which are tricky and time-consuming.
2. You can use this tool for educational purposes and solve many other real-life problems.
3. You can use this tool to calculate the angle between two vectors.
4. You don’t have to pay any fee to use it because it is free of cost.
5. Cross product calculator is easy to use because it contains simple and easy steps. You have to enter the values of the components of the vectors; it will process them faster and give the result accurately.
6. Cross product 2 vectors calculator is fully reliable because there is no chance of error in its solution.

## What is a vector product?

The vector product is the product of two vectors multiplied together to find their resultant vector. A cross denotes it as ‘’. Its formula is:

$$\vec A \;X\; \vec B \;=\; |A||B|sinθ$$

## What is the difference between vector and scalar products?

The difference is that the vector product of two vectors results in another vector. But the scalar product of two vectors results in a scalar quantity or number.

### Shaun Murphy

Last Updated March 28, 2022

A professional content writer who likes to write on science, technology and education.