Vector A
Vector B
Vector C = A × B

Cross Product Calculator

In Physics, some types of multiplications related to vectors are involved to solve complex problems. One of those types is the cross-product of vectors that results in a vector at the end of the process. But it is not an easy task as the product involves an angle and components of the vector. That’s why it is common to make mistakes and get a wrong answer in the end.

In this regard, you can use a cross-product calculator that has been designed for this particular type of vector multiplication. With the help of this maths calculator, you can find the multiplication of two vectors with three components in the x, y, and z directions. You only have to put the values of components and the calculator will multiply them quickly without clicking on any button. Let’s read about cross-product and the use of this cross-product calculator in detail.

What is the cross-product?

It is a particular type of vector multiplication in which two vectors will result in another final vector. As the answer of the cross product is a vector, that’s why it is also called a vector product. The components of the resultant vector depend on the components of the vectors that are going to be multiplied.

When it comes to vector products, another type of multiplication involves that results in a scalar quantity as the resultant. It is called the dot product of vectors. Both these types of products are the multiplication of two vectors with three-dimensional components.

Cross product formula

To find the cross-product of two vectors, you have to follow a specific formula. Let us share a general formula for this type of vector product for two vectors “A” and “B”.

						A x B = |A| |B| sin θ n 					

Here:

  • The bold letters represent the vectors.
  • The vertical lines show the scalar values of vectors.
  • “θ” is the angle between “A” and “B”.
  • “n” shows the unit vector in the direction of the resultant vector.

By using this formula, you can find the cross product of any two vectors.

Example of the cross product

To let you understand the process properly, we have solved an example here. Go through it and check how this product is performed.

Example 1:

Find the cross product of two vectors with components (2, 5, 7) and (1, 5, 4) while the angle between them is 90 degrees.

Solution:

Suppose, the given vectors are “A” and “B”. So, we can follow the above-mentioned formula

						A x B = |A| |B| sin θ n

To get the answer, we need to multiply the “x” component of the first vector with the “x” component of the second vector. Similarly, the process will be repeated for the “y” and “z” components.

						= (2 x 1)i - (5 x 5)j + (7 x 4)k (sin 90) 

Also, we know that,

						Sin 90 = 1							

So, the resultant vector will be:

						A x B = 2i -25j +28k							

Here, “i”, “j”, and “k” shows the “x”, “y”, and “z” components of the resultant vector.

How to use the cross-product calculator?

To use this tool by Calculator’s Bag, you only have to follow these simple steps.

  • Insert the components of the first vector
  • Insert the components of the second vector
  • The calculator will automatically multiply your given vectors and show you the resultant.

FAQ | Cross Product Calculator

How do you find the cross-product?

To find the cross product of two vectors, you can follow this formula.

						A x B = |A| |B| sin θ n 						

Does cross-product depend on order?

Yes, the order of vectors directly impacts the answer of the cross-product. It is because the direction of the vector will be reversed by changing the order of the vectors.

What happens if the cross-product is 1?

If the cross product is 1, it means that the given vectors are perpendicular to each other because “Sin 90” is “1”.

Does the cross-product always result in a vector?

Yes, the cross-product always gives a vector as the result. On the other side, the dot product always gives a scalar value at the end of the multiplication.

Why does the cross-product produce a perpendicular vector?

Cross-product is the multiplication of the two vectors. To find the direction of the resultant vector, the Right-hand rule is used. It shows that the direction of the resultant vector will be perpendicular to the given vectors.