What is the Cross Product of Two Vectors?
Cross-product is one of the most common tasks when it comes to vector Mathematics or Physics. It has great importance in different professional and practical fields. That’s why it is important to learn how to find the cross-product of two vectors.
If you don’t know, you should read this blog as we will discuss it here. When two vectors are multiplied, they can either give a scalar resultant or a vector resultant. In the cross product, when two vectors are multiplied, we will get a vector as the answer that has a specific direction.
The cross product between two vectors is represented by putting a symbol of “x”. It also involves the angle between the vectors to find the resultant. For example, the cross product of perpendicular vectors is maximum while the cross product of parallel vectors will be
Method to find the cross product of two vectors
Finding the cross product of two vectors may not be difficult if you know the formula. Here in this section, we are going to show you the formula for this product if you have two vectors
= AB sin𝜽 n
Here in this formula, “𝜽” represents the angle between the vectors while “n” is the unit vector that gives the direction of the resultant vector. Using this cross-product formula, you can find the resultant of the multiplication of any two vectors.
If you are unable to understand the formula or have complex values to deal with, you should use an online cross-product calculator available in our maths calculator.
It will help you in getting the answer to the multiplication within seconds. The tool has been designed with a simple interface to let everyone understand and use it seamlessly.
How to calculate the cross-product of two vectors?
To help you in understanding the process, we have also solved an example here. You should check it and try to understand the process step by step.
Example 1:
Find the cross product of two vectors having coordinates (2, 5, 8) and (3, 7, 9) while the angle between
them is 90 degrees.
Solution:
We only have to multiply the coordinates of the points/vertices given in the question and find the solution for the angle.
Suppose, the vectors are named "A" and "B" So,
A x B = (2 x 3)i - (5 x 7)j + (8 x 9)k
Also,
Sin 90 = 1
So, the overall answer will become:
A x B = 6i - 35j + 72k
In this answer, "i", "j", and "k" represent the x-y-z coordinates of the resultant vector.
Conclusion
By reading this blog, you have learned the way to find the cross product of two vectors. We have shared a solved example too for your better understanding. If you want to check more examples like this, you should use the cross product of two vectors calculator and put your concerned values. It will help you in understanding the solution deeply.
FAQ
1. What is a cross-product with an example?
The cross product of two vectors is the vector product in which two vectors when multiplied give another vector.
2. What is the rule of the cross-product?
&For vector products, you only need to know the coordinates of the vectors and the angle between them.
3. What are the properties of the cross-product?
- The cross product of two vectors will always give another vector.
- The vector product of two perpendicular vectors is the maximum.
- The cross product of two parallel vectors is “0”.
4. What is the difference between dot and cross product?
When two vectors are multiplied and they give a scalar quantity, it will be called the dot product. On the other side, if two vectors give another vector when multiplied, it is called a cross product.
5. Does the cross-product always result in a vector?
Yes, the cross-product will always result in a vector.
6. What is the cross product of the two vectors formula?
The cross product of the two vectors formula is given below,
A×B sin𝜽 n
