(1) The angle between the direction in which a craft is moving and the longitudinal axis of the craft. (2) The angle between the projection, onto a horizontal plane, of the direction in which a craft is moving the projection, onto the same plane, of the longitudinal axis of the craft. The angle is usually small enough that either of the definitions gives the same angle within the tolerances allowed by the situation. (3) The angle through which a coordinate system fixed in a photograph must be rotated about the z-axis in object space to make the x-axis and y-axis of the photograph parallel to the x-axis and y-axis in object space. Yaw is usually the tertiary rotation, preceded by pitch and roll, so that the photograph's z-axis is presumed already to have been made parallel to the z-axis in object space. (4) The angle through which a coordinate system fixed in a photograph is rotated about a specified line through the origin of the coordinate system and nearly perpendicular to the photograph. The angle is measured in a plane perpendicular to the specified axis of rotation between a specified line in that plane and the projection of the x axis of the coordinate system of the photograph onto that plane. In all the above definitions, the angle, also called crab is usually denoted by _k and called kappa.