Tangent - Tangent, Normal and Binormal Vectors In this...

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Tangent, Normal and Binormal Vectors In this section we want to look at an application of derivatives for vector functions. Actually, there are a couple of applications, but they all come back to needing the first one. In the past we’ve used the fact that the derivative of a function was the slope of the tangent line. With vector functions we get exactly the same result, with one exception. Given the vector function, , we call the tangent vector provided it exists and provided . The tangent line to at P is then the line that passes through the point P and is parallel to the tangent vector, . Note that we really do need to require in order to have a tangent vector. If we had we would have a vector that had no magnitude and so couldn’t give us the direction of the tangent. Also, provided , the unit tangent vector to the curve is given by, While, the components of the unit tangent vector can be somewhat messy on occasion there are times when we will need to use the unit tangent vector instead of the tangent vector. Example 1
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This note was uploaded on 11/10/2011 for the course MATH 136 taught by Professor Prellis during the Fall '08 term at Rutgers.

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Tangent - Tangent, Normal and Binormal Vectors In this...

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