zcomponent

The z-component, or z-component, is the component of a three-dimensional vector along the z-axis of a Cartesian coordinate system. If a vector is written as v = (v_x, v_y, v_z), the z-component is v_z, equivalently the projection of v onto the unit vector k = (0, 0, 1). The z-component can be computed as v_z = v · k.

Geometrically, the z-component represents the length of the projection of the vector onto the z-axis. In other words, it is the portion of the vector that points in the z direction. If the vector is described in spherical coordinates with magnitude |v| and polar angle theta measured from the positive z-axis, then v_z = |v| cos(theta).

Examples help illustrate the idea: the vector v = (3, -2, 5) has a z-component of 5. The position vector r = (x, y, z) has a z-component equal to z. The z-component can be important in physics and engineering for analyzing motion, forces, and fields, as well as in computer graphics and data processing where depth or vertical projection matters.

Note that the meaning of the z-axis depends on the chosen coordinate convention; in some contexts z may point up, into the screen, or along another direction. Nonetheless, the z-component always denotes the projection of a quantity onto the designated z-axis. In computing contexts, a vector’s z-component is commonly denoted as z, r_z, or v_z, and is often accessed as the third element of the vector.