Let F be the vector fields shown in the figure. (a) If C 1 is the vertical line segment from ( − 3 , − 3 ) to ( − 3 , 3 ) , determine whether ∫ C 1 F ⋅ d r is positive, negative, or zero. (b) If C 2 is the counterclockwise-oriented circle with radius 3 and center the origin, determine whether ∫ C 2 F ⋅ d r is positive, negative, or zero.
Let F be the vector fields shown in the figure. (a) If C 1 is the vertical line segment from ( − 3 , − 3 ) to ( − 3 , 3 ) , determine whether ∫ C 1 F ⋅ d r is positive, negative, or zero. (b) If C 2 is the counterclockwise-oriented circle with radius 3 and center the origin, determine whether ∫ C 2 F ⋅ d r is positive, negative, or zero.
Solution Summary: The author explains that the line integral of F along C is positive.
(a) If C1 is the vertical line segment from
(
−
3
,
−
3
)
to
(
−
3
,
3
)
, determine whether
∫
C
1
F
⋅
d
r
is positive, negative, or zero.
(b) If C2 is the counterclockwise-oriented circle with radius 3 and center the origin, determine whether
∫
C
2
F
⋅
d
r
is positive, negative, or zero.
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
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