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1. Compute the Frenet apparatus k, 7, T, N and B of the following curve √2 a(s) = (1 – ½ c cos s, 3 + cos s, sin s). 2 Show that this curve is a circle and find its center and radius.

1. Compute the Frenet apparatus k, 7, T, N and B of the following curve √2 a(s) = (1 – ½ c cos s, 3 + cos s, sin s). 2 Show that this curve is a circle and find its center and radius.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1. Compute the Frenet apparatus k, T,T, N and B of the following curve a(s) = (1 cos s, 3 + cos s, sin s). 2 Show that this curve is a circle and find its center and radius. 2. Consider the level surface S definned by f(x, y, z) = 0, where f is smooth and its partial derivatives do not all vanish at any point of S. Show that the gradient vector Vf(r, y, z) = (fz; fy, fz) is perpenducu- lar to the tangent plane T„S at any point p in S.
Transcribed Image Text:1. Compute the Frenet apparatus k, T,T, N and B of the following curve a(s) = (1 cos s, 3 + cos s, sin s). 2 Show that this curve is a circle and find its center and radius. 2. Consider the level surface S definned by f(x, y, z) = 0, where f is smooth and its partial derivatives do not all vanish at any point of S. Show that the gradient vector Vf(r, y, z) = (fz; fy, fz) is perpenducu- lar to the tangent plane T„S at any point p in S.
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