Mathematical Analysis

Vector and Other Analyses

What is a normalized vector?

A normalized (or unit) vector is one in which the sum of the squares of all coordinates is equal to one. For example, the vector (2, 2, 0) is not normalized; the vectors (0.707, 0.707, 0.0) and (1.0, 0.0, 0.0) are normalized. (An outward normal is another name for a normalized vector; it represents the direction that a polygon surface or vertex [end-point] is facing.) Normalized (or unit) vectors are often seen written as Image, but more usually as Image (the Image is often referred to as a “hat”).

A vector can be normalized by calculating the magnitude or length of the vector and dividing each coordinate by this value. For example, consider the following vector:



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