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Unformatted text preview: Pay Chris Leger $1 Anyone catch the typo on the homework assignment? ..?.. Theres a (vector) that should be a 0 (scalar) in problem B. Section 10.7: Vector functions and space curves Main ideas of 563567? ..?.. The vector derivative and the unit tangent vector Properties of the derivative (Theorems 4 and 5) The definition of the tangent line to a space curve The geometric interpretation of the tangent vectors for smooth curves Integrals of vector functions Show Secant and Tangent Vectors The unit tangent vector is r ( t )/| r ( t )|. Consider the curve r ( t ) = sin t cos t , cos 2 t , sin t . Why is | r ( t )| constant? ..?.. sin 2 t cos 2 t + cos 4 t + sin 2 t = cos 2 t (sin 2 t + cos 2 t ) + sin 2 t = cos 2 t + sin 2 t = 1. What does this tell us about the angle between r ( t ) and T ( t )? ..?.. Hint: Use Example 12....
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