Magnitude of a Vector

The magnitude (also called the norm) of a vector is the length of the arrow representing it — always a non-negative real number, regardless of which way the vector points. For a vector $\vec A$, the magnitude is written $|\vec A|$, or more simply just $A$ (the same letter without the arrow/boldface). If $\vec A$ is broken into rectangular components $A_x, A_y, A_z$, its magnitude is found from the three-dimensional Pythagoras theorem:

$A = |\vec A| = \sqrt{A_x^2 + A_y^2 + A_z^2}$ …