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T(t)= (1,1,2t), 0≤t≤ 2. √1+51² Suppose that the tangent vector of r(t) has magnitude ✓1+5t². (a) (b) (c) (d) Find the curvature K of the curve r(t) at a general point 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.

T(t)= (1,1,2t), 0≤t≤ 2. √1+51² Suppose that the tangent vector of r(t) has magnitude ✓1+5t². (a) (b) (c) (d) Find the curvature K of the curve r(t) at a general point 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.

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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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.
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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