Normalized Vector

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Section 8.1 Normalized Vector

A normalized vector is a vector that has been scaled to have a norm of 1 (hence the name unit vector). This is often done to simplify calculations or to ensure that the vector represents only a direction without any magnitude. Normalizing a vector involves dividing each component of the vector by its norm (or magnitude).

The normalized vector is a unit vector that points in the same direction as the original vector. Normalizing a vector means scaling it so that it has length $1$ while preserving its direction. This is useful in applications such as directional vectors, unit vectors, and simplifying computations involving angles or projections.

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