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.