Answer
FALSE.
Work Step by Step
For a conservative vector field,
$$ \int_{C} F.Tds = 0 $$ over any closed path Thus $F$ and $T$ may not be orthogonal.
Calculus 10th Edition
by Larson, Ron; Edwards, Bruce H.
Published by
Brooks Cole
ISBN 10:
1-28505-709-0
ISBN 13:
978-1-28505-709-5
Chapter 15 - Vector Analysis - 15.2 Exercises - Page 1064: 86
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