Length of a Vector Calculator Online

The Length of a Vector Calculator is designed to compute the magnitude of a vector based on its components. This tool is helpful for calculating the length of vectors in both simple two-dimensional cases and more complex scenarios involving higher dimensions. It is especially useful in educational settings for verifying manual calculations and in professional environments where efficient and accurate calculations are necessary.

Formula of Length of a Vector Calculator

To calculate the length or magnitude of a vector, use the following mathematical formula:

For a vector v = (v1, v2, ..., vn), the length is calculated by:

Length = sqrt(v1^2 + v2^2 + ... + vn^2)

• In a 2-dimensional space, for a vector v = (v1, v2), the formula simplifies to:

Length= sqrt(v1^2 + v2^2)

• In a 3-dimensional space, for a vector v = (v1, v2, v3), the formula is:

Length = sqrt(v1^2 + v2^2 + v3^2)

• In a 4-dimensional space, for a vector v = (v1, v2, v3, v4), the formula is:

Length= sqrt(v1^2 + v2^2 + v3^2 + v4^2)

• In a 5-dimensional space, for a vector v = (v1, v2, v3, v4, v5), the formula is:

Length = sqrt(v1^2 + v2^2 + v3^2 + v4^2 + v5^2)

Table for General Terms and Useful Conversions

Here is a table of common vector lengths in different dimensions, along with other relevant calculations or conversions that might be useful for users:

Vector Dimension	Example Vector	Length Calculation Result
2D	(3, 4)	5
3D	(1, 2, 2)	3
4D	(1, 1, 1, 1)	2
5D	(2, 2, 2, 2, 2)	4.47

Examples of Length of a Vector Calculator

1. 2D Vector: For a vector (3, 4),
   • Calculation: Length = sqrt(3^2 + 4^2) = sqrt(9 + 16) = sqrt(25) = 5
2. 3D Vector: For a vector (1, 2, 2),
   • Calculation: Length = sqrt(1^2 + 2^2 + 2^2) = sqrt(1 + 4 + 4) = sqrt(9) = 3

These examples demonstrate how the calculator simplifies the process of finding vector lengths, making it more accessible and less time-consuming.

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