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# 09.23 - Pay Chris Leger \$1 Anyone catch the typo on the...

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Pay Chris Leger \$1 Anyone catch the typo on the homework assignment? ..?.. There’s a 0 (vector) that should be a 0 (scalar) in problem B. Section 10.7: Vector functions and space curves Main ideas of 563–567? ..?.. 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 = …

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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. ..?.. Example 12 tells us that if | r ( t )| is constant (as is the case here), r ( t ) is orthogonal to r ( t ). But T ( t ) points in the same direction as r ( t ), so r ( t ) is orthogonal to T ( t ) as well.
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09.23 - Pay Chris Leger \$1 Anyone catch the typo on the...

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