## Vectors in 3-D Coordinate Systems

Vectors represent quantities such as velocity and acceleration. Mapping Toolbox™ functions transform vector components between Earth-centered Earth-fixed (ECEF) and east-north-up (ENU) or north-east-down (NED) systems. For more information about ECEF, ENU, and NED coordinate systems, see Comparison of 3-D Coordinate Systems.

Unlike coordinates that measure position, vector components in a Cartesian system do not depend on a position in space. Therefore, when you transform a vector from one system to another, only the components of the vector change. The magnitude of the vector remains the same.

For example, this image shows a 2-D vector transformation from an
*x*-*y* system to a
*u*-*v* system. The vector has components
*x* = 2 and *y* = 1 in the
*x*-*y* system, and components *u*
= 1.30 and *v* = 1.82 in the *u*-*v*
system. The components of the vector are different, but in each system the magnitude of the
vector is 2.24 units.

This image shows a coordinate transformation from a global ECEF system to a local ENU
system using `ecef2enu`

. The position vectors start at the origin
of each system and end at point *P*. Therefore, the transformation changes
the magnitude of the position vector.

This image shows a vector transformation from a global ECEF system to a local ENU system
using `ecef2enuv`

. The vector **r** does not depend on a position. Therefore, the transformation changes the
components of the vector, but the magnitude of the vector is the same.

### Tips

Unlike coordinate transformation functions such as `ecef2enu`

, vector transformation functions such as `ecef2enuv`

do not require you to specify a reference spheroid or the
ellipsoidal height of the local origin. The geodetic latitude and longitude of the local
origin is sufficient to define the orientation of the *uEast*,
*vNorth*, and *wUp* axes.

## See Also

`enu2ecefv`

| `ned2ecefv`

| `ecef2nedv`

| `ecef2enuv`