r(t) : (x(t), y(t), z(t)) where x(t) = – 2t + 3t + 3 y(t) = 2t – 2 z(t) = 2t2 + 5t Since all components are of no higher degree than quadratic, r'''(t) = torsion of this curve is zero. This means the binormal vector B < 0, 0,0 > and so the B(t) is constant, and that the curve lies in a single plane.

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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This is a calculus 3 problem. Please explain each step clearly, no cursive writing. 

r(t) = (x(t), y(t), z(t)) where
– 2t? + 3t + 3
æ(t)
y(t) = 2t – 2
z(t) = 2t? + 5t
= -
(t) = < 0,0, 0 > and so the
B(t) is constant, and that the
Since all components are of no higher degree than quadratic, r
torsion of this curve is zero. This means the binormal vector B
curve lies in a single plane.
Transcribed Image Text:r(t) = (x(t), y(t), z(t)) where – 2t? + 3t + 3 æ(t) y(t) = 2t – 2 z(t) = 2t? + 5t = - (t) = < 0,0, 0 > and so the B(t) is constant, and that the Since all components are of no higher degree than quadratic, r torsion of this curve is zero. This means the binormal vector B curve lies in a single plane.
c) Find the maximum curvature of this curve.
K max
Transcribed Image Text:c) Find the maximum curvature of this curve. K max
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