Magnitude of a Vector

Definition: The magnitude of a vector (||v||)  defines its length or size. Magnitude is always greater than or equal to zero.

The magnitude of a vector (||v||) in component form can be found using the following formula:

Given the coordinates of a vector’s initial and terminal points, the distance formula can be used to find magnitude:

Example: Find the magnitude of the vector a:

a = <2, -3>.

Solution:

To find the magnitude of vector A, plug in the two components into the formula:

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