Vector Magnitude Calculator

An online vector magnitude calculator helps you to determine the magnitude of 2D, 3D, 4D, and 5D vectors by the given coordinates or points of vector representation. Also, this length of vector calculator computes the vector by initial and terminal points by using its formula. Read on to learn how to find the magnitude of a vector. Let’s start with some basics!

What is the Magnitude of a Vector?

A vector has magnitude (length) and direction. In order to find the magnitude of the vector, we need to calculate the length of the vector. Quantities such as displacement, velocity, momentum, and force, etc. are all vector quantities. But Mass, volume, distance, temperature, etc. are scalar quantities. The scalar has only magnitude, and it has the same direction and magnitude. The magnitude of a vector formula is used to determine the length of this vector and is used to represent | v |, so this value is basically the length between the start and terminal point of the vector.

The Magnitude of a Vector Formulas:

Suppose AB is a vector quantity that has both direction and magnitude. In order to calculate the magnitude of the vector AB, we need to calculate the distance between the start point A and the endpoint B. In the XY plane, let A coordinate (a_x^0, b_y^0) and B coordinate (a_x^1 and b_x^1). Therefore, using the distance formula, the magnitude of the vector AB can be written as:

AB | = \ sqrt {(a_x-a_y)^ 2 + (a_y – b_y)^ 2}

The magnitude of the vector | AB | can be estimated in different ways. According to the dimensionality of the vector space, we have:

|AB| = \sqrt {(a_x^2 + b_y^2)} in 2-d space

|AB| = \sqrt {(a_x^2 + b_y^2 + c_z^2)} in 3-d space

|AB| = \sqrt {(a_x^2 + b_y^2 + c_z^2 + d_t^2)} in 4-d space

|AB| = \sqrt {(a_x^2 + b_y^2 + c_z^2 + d_t^2 + e_w^2)} in 5-d space, and so on…

These are some formulas for different dimensions which are used by the vector magnitude calculator.

However, an Online Angle Between Two Vectors Calculator allows you to find the angle, magnitude, and dot product between the two vectors.

How to Find the Magnitude of a Vector?

The number of vector components depends on the dimensions of the space. We usually deal with 2D and 3D vectors with three different components. In Cartesian coordinates, we can use the values of a, b, and c components. In order to obtain the spherical coordinates, it is convenient to use the values of the two angles θ and φ and the vector length in the purest sense. In other words, the three-dimensional distance between the start and end of the vector.

However, use Distance Formula Calculator that assists you in computing the distance among any two points.

How Vector Magnitude Calculator Works?

An online magnitude of a vector calculator finds the length of vectors for entered coordinates or initial and terminal points by following these instructions:

Input:

First, select any required dimension of a vector from the drop-down list.
Now, select the vector representation either by coordinates or by points.
Then, substitute all the required values in the corresponding fields.
Hit the calculate button to see the all calculations.

Output:

The vector magnitude calculator provides the length of a vector.
It displays the magnitude of a vector formula for calculating its length with step-by-step calculations.

FAQ:

What are the types of vectors?

Types of Vectors List

Null Vector
Unit Vector
Co-initial Vector
Position Vector
Collinear Vector
Co-planar Vector
Like and Unlike Vectors
Equal Vector

What is vector explain with example?

A vector is a quantity with two independent properties: magnitude and direction. The examples of vectors in nature are momentum, velocity, force, weight, and electromagnetic fields.

Are there directions for the dimensions?

A quantity that does not depend on direction is called a scalar quantity. Vector quantities have two attributes, direction, and magnitude. Scalar quantities just have a magnitude. When comparing two vector quantities, you have to compare both the direction and the magnitude.

How do you define magnitude?

In physics, magnitude is described in simple terms, such as quantity or distance. Magnitude is the absolute or relative amount of movement of an object in the sense of its movement. It is mostly used to describe the size or extent of something.

Conclusion:

Use this online vector magnitude calculator for computing the magnitude (length) of a vector from the given coordinates or points. The magnitude of the vector can be calculated by taking the square root of the sum of the squares of its components. When it comes to calculating the magnitude of 2D, 3D, 4D, or 5D vectors, this magnitude of a vector calculator is essential to make your calculation simple.

Reference:

From the source of Wikipedia: Magnitude, Real & Complex numbers, Vector spaces, Euclidean vector space, Normed vector spaces.

From the source of Khan Academy: Pseudo-Euclidean space, Logarithmic magnitudes, Order of magnitude, Vector components from magnitude & direction.

From the source of Libre Text: vectors geometrically, magnitude and direction, vector addition and scalar multiplication, the dot product of two vectors.