Let I be the curve parametrised by 2t 2(4) = ( sin(zt), 41' Vt +1 for 0

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Let I be the curve parametrised by
y(t) :
sin(πt ),
2t
Vt + 1
for 0<t<1
t2 +1°
and let F be the vector field
F(x, y, z) = (a – 422x)i+ 2byj + cx²zk
where a,
b and c are real numbers.
(a) Find all values of a, b and c such that the vector field F is conservative.
(b) If a, b and c are chosen such that F is conservative, compute the work done by F to move
a particle along I' in the direction of increasing t.
Transcribed Image Text:Let I be the curve parametrised by y(t) : sin(πt ), 2t Vt + 1 for 0<t<1 t2 +1° and let F be the vector field F(x, y, z) = (a – 422x)i+ 2byj + cx²zk where a, b and c are real numbers. (a) Find all values of a, b and c such that the vector field F is conservative. (b) If a, b and c are chosen such that F is conservative, compute the work done by F to move a particle along I' in the direction of increasing t.
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