Calculate the modulus of a vector is an operation that you will have to use in many math exercises, such as calculating the scalar product of two vectors. Below is a calculator that allows you to obtain the modulus of a vector from its components (v1, v2) or the position of two of its points A (x1, y1) and B (x2, y2)
You only have to type in our calculator the vector data you know and press the calculate button to obtain its modulus. Also, if you want to learn how to calculate the modulus of a vector we show you how it is done.
Article sections
What is the modulus of a vector?
When we talk about the modulus of a vector we are referring to the length of the segment that lies between its ends A and B:
When calculating the modulus, we will always obtain a positive value or equal to zero if it is a null vector.
How to calculate the modulus of a vector with its components
A vector is defined by its components and from these components we can calculate its modulus by applying the following formula:
Basically what you have to do is to calculate the square root of the sum of each component squared.
For example, we are going to calculate the square root of two vectors 
= (3, 0) y 
= (5, 5):
If the vector is three-dimensionalThe formula to calculate its modulus is exactly the same but adding the square of that third component. That is, you would have to apply this equation:
In the case of a vector in R3If the x, y, and z components are squared, we will calculate the square root of the sum of the x, y, and z components squared.
Calculate the modulus of a vector from the coordinates of two points.
There is a second method for to get the modulus of a vector from the coordinates of two of its points. We only have to apply the following formula:
As a solved exercise, we are going to calculate the modulus of a vector whose points are A(2, 1) and B(-3, 2). We apply the formula that we have just in the image above these lines and we have that:
¿Y how is it calculated if the coordinates are three-dimensional?? In the case that each of the points of the vector has coordinates x, y, z, then the formula to use is this:
The process is exactly the same than in the two-dimensional case, although the equation takes into account this third coordinate of the Z-axis.
Modulus of the sum of two vectors
For calculate the modulus of the sum of two vectors we have to:
- Calculate the square of the modulus of each vector
- Calculate the scalar product of the two vectors
Once we have it, we apply the following mathematical formula:
If you have any doubt about how to get the modulus of a vector from its components or coordinates, leave us a comment and we will be happy to help you.
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