Finding the Magnitude of Vectors | Calculations and Methods Explained

The magnitude of a vector =

In mathematics, the magnitude of a vector refers to the length or size of the vector

In mathematics, the magnitude of a vector refers to the length or size of the vector. It represents the numerical value of the vector without considering its direction.

The magnitude of a vector can be found using various methods, depending on the coordinate system or representation used. For example, in a two-dimensional Cartesian coordinate system, the magnitude of a vector is calculated using the Pythagorean theorem.

If we have a vector represented by its components as (x, y), the magnitude (denoted as ||v||) can be calculated as:

||v|| = √(x^2 + y^2)

In a three-dimensional Cartesian coordinate system, where the vector has components (x, y, z), the magnitude can be calculated as:

||v|| = √(x^2 + y^2 + z^2)

The magnitude of a vector is always a non-negative value. It gives us information about the overall “length” or “size” of the vector, regardless of its direction.

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