The resultant vector is the vector that 'results' from adding two or more vectors together. There are a two different ways to calculate the resultant vector. Methods for calculating a Resultant Vector: The head to tail method to calculate a resultant which involves lining up the head of the one vector with the tail of the other.

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Then, the tangent vector of αis α˙ (s) = cosφ(s),sinφ(s) , which is a unit vector making an angle φ(s) with the x-axis. Thus αis unit speed, and has curvature dφ ds = d ds Z s s0

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The unit tangent vector T. The velocity vector v(t) is tangent to the curve and its length is the speed. If we scalar multiply the velocity by (1/speed), we get a unit vector T tangent to the curve. We can view T as a function of time t or as a function of position s along the curve. T(t) = v(t) kv(t)k. In our spiral curve example, we have

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...3-8, find the unit tangent vector to the curve at the specified value of the parameter. r ( t ) = e t cos t i + e t j , t = 0. 12.1 Vector-valued Functions 12.2 Differentiation And Integration Of Vector-valued Functions 12.3 Velocity And Acceleration 12.4 Tangent Vectors And Normal Vectors 12.5 Arc...

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unit tangent vector T t is the unit vector in the direction of t . That is, if the speed is non zero, then we can define T t to be T t 1 | t | t s 1 s x t ,y t ,z t . This is also called the tangent vector field , because it gives a vector at each point t of the curve (i.e. all points, not just one point of the curve).

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tangent to the graph of the function. Thus, it is natural to expect that, when dealing with vector functions, the derivative will give a vector whose direction is tangent to the graph of the function. However, since the same curve may have di erent parametrizations, each of which will yield a di erent derivative at a given