Chapter 11: Q. 38 (page 860)
Evaluate and simplify the indicated quantities in Exercises 35–41.
The simplification of is .
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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 as t increases. Find another parametrization for this helix so that the motion is downwards.
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.
Prove that the tangent vector is always orthogonal to the position vector for the vector-valued function.
Evaluate and simplify the indicated quantities in Exercises 35–41.
Let Cbe the graph of a vector-valued function r. The plane determined by the vectors and containing the point is called the normal plane forC at. Find the equation of the normal plane to the helix determined byfor.
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