# Translations:The unit tangent vector/8/en

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Let us review the results. Let the vector **r** be a point on the raypath. A closely spaced point on the raypath can be represented by the vector . Their difference is the vector , which is the vector that connects the two points in question. Let the path length between the two points be *ds*. The unit tangent to the raypath is the limit as the points approach each other. The length of the vector is approximately equal to the path-length difference *ds*. As a result, the vector is the unit vector. Let be the angle that the tangent makes with the horizontal axis. The unit tangent vector is then . The vector **u** is directed along the tangent to the curve in the direction of increasing values of the arc length *s*.