ühikvektorid

ühikvektorid, also known as unit vectors, are vectors with a magnitude (or length) of exactly one. They are fundamental in many areas of mathematics and physics, particularly in linear algebra and vector calculus. The primary purpose of a ühikvektor is to indicate direction. Multiplying a ühikvektor by a scalar quantity preserves the direction but scales the magnitude to that of the scalar.

In a given coordinate system, ühikvektorid are often used to represent the axes. For example, in a three-dimensional Cartesian coordinate system, the standard ühikvektorid are denoted by i, j, and k. The vector i points along the positive x-axis, j along the positive y-axis, and k along the positive z-axis. Any vector in this space can be expressed as a linear combination of these standard ühikvektorid.

To obtain a ühikvektor in a specific direction, one divides any non-zero vector lying along that direction by its magnitude. The formula for a ühikvektor u in the direction of a vector v is u = v / ||v||, where ||v|| represents the magnitude of vector v. This process normalizes the vector, retaining its direction while setting its length to one. Ühikvektorid are essential for defining orthonormal bases and simplifying complex vector operations.