r(t) = (x(t), y(t), z(t)) where = - 4t? – 5t – 3 æ(t) - 5t2 + 5t + 3 y(t) = - 5t? z(t) : || Since all components are of no higher degree than quadratic, r'"(t) < 0, 0,0 > and so the B(t) is constant, and that the torsion of this curve is zero. This means the binormal vector B 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
– 4t2 – 5t – 3
¤(t)
y(t) = 5t + 5t + 3
z(t) = – 5t2
-
(t) =
< 0, 0, 0 > and so the
Since all components are of no higher degree than quadratic, r
torsion of this curve is zero. This means the binormal vector B = B(t) is constant, and that the
curve lies in a single plane.
Transcribed Image Text:r(t) = (x(t), y(t), z(t)) where – 4t2 – 5t – 3 ¤(t) y(t) = 5t + 5t + 3 z(t) = – 5t2 - (t) = < 0, 0, 0 > and so the Since all components are of no higher degree than quadratic, r torsion of this curve is zero. This means the binormal vector B = B(t) is constant, and that the 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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