Chapter 11: Q. 36 (page 860)
Evaluate and simplify the indicated quantities in Exercises 35–41.
Short Answer
The simplification of is .
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Chapter 11: Q. 36 (page 860)
Evaluate and simplify the indicated quantities in Exercises 35–41.
The simplification of is .
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For each of the vector-valued functions, find the unit tangent vector.
Prove that the cross product of two orthogonal unit vectors is a unit vector.
As we saw in Example 1, the graph of the vector-valued function is a circular helix that spirals counterclockwise around the z-axis and climbs ast increases. Find another parametrization for this helix so that the motion along the helix is faster for a given change in the parameter.
In Exercises 19–21 sketch the graph of a vector-valued function with the specified properties. Be sure to indicate the direction of increasing values oft.
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Find parametric equations for each of the vector-valued functions in Exercises 26–34, and sketch the graphs of the functions, indicating the direction for increasing values of t.
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