**scalar or dot product**and the other is the

**cross or vector product**. A

**scalar product**is a physical quantity that returns a scalar value after multiplying two vectors. In comparison, the

**vector product**is a physical quantity that returns a vector after multiplying two vectors.

Computing the product of large vectors is not an easy task. It may require large calculations and time while computing it manually. However, in todayâ€™s era of high computing tools, we are blessed with MATLAB which makes many calculations in the shortest amount of time using the built-in functions. One such function is the **cross() **which allows us to determine the cross product of two vectors.

This tutorial will discover:

- What is the Cross-Product?
- Why We Need to Determine the Cross product?
- How to Determine the Cross Product of Two Vectors in MATLAB?
- Examples
- Conclusion

**What is the Cross-Product?**

The **cross-product** of two vectors is a physical quantity that is calculated by multiplying two vectors. It returns a vector** perpendicular** to the given two vectors. If **A **and** B **are two vector quantities, their cross-product C is given as:

Where** C** is also a vector quantity and it is perpendicular to both** A **and** B**.

**Why We Need to Determine the Cross product?**

The **cross-product** performs many tasks in physics, mathematics, and engineering. Some of them are given below.

The **cross-product** is used to find:

- The area of a triangle.
- The angle between two vectors.
- A unit vector perpendicular to two vectors.
- The area of a parallelogram.
- Collinearity between two vectors.

**How to Implement the cross product of Two Vectors in MATLAB?**

MATLAB facilitates us with a built-in **cross()** function to find the **cross product** of two vectors. This function accepts two vectors as mandatory inputs and provides their **cross-produc**t in terms of vector quantity.

**Syntax**

The **cross()** function can be implemented in MATLAB through the given ways:

Here,

The function **C = cross(A,B) **is responsible for calculating the **cross product C** of the given vectors **A** and **B**.

- If
**A and B**represent vectors, they must have a**size**equal to**3**. - If
**A and B**represent two matrices or multidirectional arrays, they must have the same size. In this situation, the**cross()**function considers**A and B**as a collection of vectors having three elements and calculates their**cross product**along the first dimension having a size equal to**3.**

The function **C = cross(A,B,dim)** is responsible for calculating the **cross product C** of the given two arrays **A and B** along the **dimension dim**. Keep in mind that **A and B** must be two arrays having the same size and **size(A,dim)**, and **size(B,dim)** must be equal to **3**. Here, **dim** is a variable containing a positive scalar quantity.

**Examples**

Consider some examples to understand the practical implementation of the **cross()** function in MATLAB.

**Example 1: How to Determine Cross Product of Two Vectors?**

In this example, we calculate the **cross-product C** of the given vectors and using the **cross()** function.

Now we can verify our result** C** by taking its **dot product** with the vectors **A and B.** If **C **is **perpendicular** to both vectors** A and B** it implies** C** is a **cross product** of **A and B**. We can check the **perpendicularity** of** C **with **A and B** by taking its **dot product** with **A and B**. If the** dot product** of** C** with **A and B** equals **0, **it implies **C** is **perpendicular** to **A and B**.

After performing the above **perpendicularity test,** we obtained a** logical value of 1** that implies the above operation is true. Hence, we conclude that the resultant vector **C** represents the **cross-product **of the given vectors** A and B**.

**Example 2: How to Determine the Cross Product of Two Matrices?**

The given example calculates the **cross-product C** of the given matrices **A,** created using the magic() function, and **B**, a matrix of random numbers, using the **cross()** function. Both matrices **A** and **B** are equal in size.

As a result, we obtain a **3-by-3** matrix **C** that is the **cross-product** of **A** and** B**. Each column of **C** represents the **cross product** of the respective columns of **A** and** B**. For example, **C(:,1)** is the** cross product** of **A(:,1) **and** B(:,1)**.

**Example 3: How to Find Cross Product of Two Multidirectional Arrays?**

The given MATLAB code determines the **cross-product C** of the given multidirectional arrays** A**, an array of random integers, and** B**, an array of random numbers, using the **cross()** function. Both arrays** A** and** B **are equal in size.

As a result, we obtain a **3-by-4-by-2** array **C** that is the **cross-product** of **A **and** B.** Each column of **C** represents the **cross product** of the respective columns of** A** and **B**. For example,** C(:,1,1)** is the cross product of **A(:,1,1)** and **B(:,1,1)**.

**Example 4: How to Find the Cross Product of Two Multidirectional Arrays Along the Given Dimension?**

Consider arrays **A** and **B** from Example 3 having size **3-by-3-by-3** and use the **cross() **function to find their **cross product** along **dimension dim=2**.

As a result, we obtain a **3-by-3-by-3** array **C** that is the **cross-product** of** A** and **B**. Each row of **C **represents the cross product of the respective rows of **A** and **B.** For example, **C(1,,1)** is the cross product of** A(1,:,1)** and **B(1,:,1)**.

**Conclusion**

Finding the **cross product** of two vectors is a common operation widely used in mathematical and engineering tasks. This operation can be performed in MATLAB using the built-in **cross()** function. This guide has explained the different ways to implement the **cross-product **in MATLAB using multiple examples.