Consider the vector function r(t) that has unit tangent vector T(x)=√1+5₁2(1,1,2r), 0≤t≤ 2. Suppose that the tangent vector of r(t) has magnitude ✓1+51². Find the curvature K of the curve r(t) at a general point t. (a) (b) Find the vector function r(t) such that r(0) = 0.
Consider the vector function r(t) that has unit tangent vector T(x)=√1+5₁2(1,1,2r), 0≤t≤ 2. Suppose that the tangent vector of r(t) has magnitude ✓1+51². Find the curvature K of the curve r(t) at a general point t. (a) (b) Find the vector function r(t) such that r(0) = 0.
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter3: Additional Topics In Trigonometry
Section: Chapter Questions
Problem 34CT: Find a unit vector u in the direction of v=i+j
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Q2 a and b
Transcribed Image Text:Consider the vector function r(t) that has unit tangent vector
1
(1,t,2t),
0<t <2.
√1+5t²
Suppose that the tangent vector of r(t) has magnitude ✓1+5t².
Find the curvature K of the curve r(t) at a general point t.
(a)
(b)
(c)
(d)
T(t)
=
Find the vector function r(t) such that r(0) = 0.
Compute the principal unit normal vector N of r(t).
Hence, determine the vector dT/ds.
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