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Excerpt
The Absolute Value

The length of a vector, or the absolute value of a scalar quantity

, which

. The magnitude is always a positive scalar value.

For instance, the velocity may be positive or negative in a one-dimensional problem, or it will be a vector in a two- or three-dimensional situation, but the speed is the magnitude of the velocity, and is always a positive scalar number.

in . The magnitude of a vector is its length[excerpt} For example, velocity is a vector whose magnitude is the speed, which is a scalar quantity that is always positive (unlike the velocity, which may be negative). In the case of uniform circular motion, the magnitudes magnitude of the position vector (when measured from the center of rotation) is constant, even though the velocity vector itself is rotating. Similarly, the magnitudes of the velocity and the acceleration vector vectors are all also constant, but their directions the vectors themselves are rotating constantly changing.