ühikuvektorid

Ühikuvektorid, also known as unit vectors, are vectors with a magnitude of one. They are used to indicate direction in a vector space. A unit vector in the same direction as a given non-zero vector v can be found by dividing v by its magnitude, denoted as ||v||. The formula for a unit vector u in the direction of v is u = v / ||v||.

In Cartesian coordinates, the standard basis vectors are the unit vectors that point along the positive x, y, and z axes. These are commonly denoted as i, j, and k respectively. The vector i has components (1, 0, 0), j has components (0, 1, 0), and k has components (0, 0, 1). Any vector in three-dimensional space can be expressed as a linear combination of these unit vectors. For example, a vector a = (ax, ay, az) can be written as a = ax i + ay j + az k.

Unit vectors are crucial in many areas of physics and engineering, such as describing forces, velocities, and electric fields. They simplify calculations by separating the magnitude of a quantity from its direction. When working with coordinate transformations or rotations, unit vectors play a fundamental role in defining the orientation of different reference frames. The concept of a unit vector is general and applies to any vector space, not just Euclidean spaces.