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Sign of a direction

When studying one-dimensional displacements and motions in analytic geometry and physics, it is common to label the two possible directions as positive and negative. Because the number line is usually drawn with positive numbers to the right, and negative numbers to the left, a common convention is for motions to the right to be given a positive sign, and for motions to the left to be given a negative sign.

On the Cartesian plane, the rightward and upward directions are usually thought of as positive, with rightward being the positive x -direction, and upward being the positive y -direction. If a displacement vector is separated into its vector components, then the horizontal part will be positive for motion to the right and negative for motion to the left, while the vertical part will be positive for motion upward and negative for motion downward.

Likewise, a negative speed (rate of change of displacement) implies a velocity in the opposite direction, i.e., receding instead of advancing; a special case is the radial speed.

In 3D space, notions related to sign can be found in the two normal orientations and orientability in general.