Egységvektora

Egységvektora is the Hungarian term for a unit vector. A unit vector is a vector that has a magnitude, or length, of one. In mathematics and physics, unit vectors are extremely useful for representing direction. When a vector is normalized to become a unit vector, its original direction is preserved, but its magnitude is scaled to be exactly 1. This is achieved by dividing the original vector by its own magnitude. For a vector v, its corresponding unit vector, often denoted as $\hat{v}$ (v-hat) or $\frac{v}{\|v\|}$, is calculated as the vector v divided by its norm (magnitude), $\|v\|$. The norm of a vector is typically calculated using the Pythagorean theorem in Euclidean space. For example, in three-dimensional space, if a vector v is represented as $(v_x, v_y, v_z)$, its magnitude is $\|v\| = \sqrt{v_x^2 + v_y^2 + v_z^2}$. Therefore, the unit vector in the direction of v would be $(\frac{v_x}{\|v\|}, \frac{v_y}{\|v\|}, \frac{v_z}{\|v\|})$. Unit vectors are often used as basis vectors in coordinate systems, such as the standard basis vectors i, j, and k in Cartesian coordinates, which represent the directions along the x, y, and z axes respectively.