Modulus of a vector

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.

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:

Vector

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

Components of a vector

A vector is defined by its components and from these components we can calculate its modulus by applying the following formula:

Formula for calculating the modulus of a vector

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 Vector u= (3, 0) y vector v= (5, 5):

Modulus of two vectors

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:

Formula for calculating the modulus of a three-dimensional vector

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:

Calculate modulus of a vector with coordinates

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:

Solved exercise of calculating the modulus of a vector

¿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:

Modulus of a three-dimensional vector

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:

Once we have it, we apply the following mathematical formula:

Modulus of the sum of two vectors

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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