Chapter 11: Q. 1 (page 901)
Sketching vector functions: Sketch the following vector functions.
On X-axis, x=t and Y-axis, y=t3
Plotting the graph,
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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.
Find the unit tangent vector and the principal unit normal vector at the specified value of t.
Prove that the tangent vector is always orthogonal to the position vector for the vector-valued function.
Every description of the DNA molecule says that the strands of the helices run in opposite directions. This is meant as a statement about chemistry, not about the geometric shape of the double helix. Consider two helices
(a) Sketch these two helices in the same coordinate system, and show that they run geometrically in different directions.
(b) Explain why it is impossible for these two helices to fail to intersect, and hence why they could not form a configuration for DNA.
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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