Egységvektorok

Egységvektorok are vectors with a magnitude (or length) of one. They are also known as unit vectors. Egységvektorok are used to indicate direction in a given space. When a vector is divided by its own magnitude, the result is a unit vector pointing in the same direction as the original vector. For example, if a vector v has magnitude |v|, the corresponding unit vector u is given by u = v / |v|.

In a two-dimensional Cartesian coordinate system, the standard egységvektorok are denoted by i and j. The vector i points in the positive x-direction and has components (1, 0). The vector j points in the positive y-direction and has components (0, 1). Any two-dimensional vector v = (vx, vy) can be expressed as a linear combination of these egységvektorok: v = vx * i + vy * j.

Similarly, in three-dimensional Cartesian coordinates, the standard egységvektorok are i, j, and k. The vector i points along the positive x-axis (1, 0, 0), j along the positive y-axis (0, 1, 0), and k along the positive z-axis (0, 0, 1). A three-dimensional vector v = (vx, vy, vz) can be written as v = vx * i + vy * j + vz * k. The concept of egységvektorok is fundamental in many areas of physics and engineering, particularly in describing forces, velocities, and fields.

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