What is magnitude of vector

The magnitude of a vector is its length. It is a non-negative scalar value. For a vector $\vec{v} = \langle v_1, v_2, \dots, v_n \rangle$ in $n$-dimensional space, its magnitude, denoted as $||\vec{v}||$, is calculated using the Pythagorean theorem:

$$||\vec{v}|| = \sqrt{v_1^2 + v_2^2 + \dots + v_n^2}$$

For example, the magnitude of the 2D vector $\vec{a} = \langle 3, 4 \rangle$ is:

$$||\vec{a}|| = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5$$