CONCEPT CHECK Line integral What is the physical significance of each line integral? a) ∫ C 1 d s b) ∫ C f ( x , y , z ) d s , where f ( x , y , z ) is the density of a string of finite length.
CONCEPT CHECK Line integral What is the physical significance of each line integral? a) ∫ C 1 d s b) ∫ C f ( x , y , z ) d s , where f ( x , y , z ) is the density of a string of finite length.
Solution Summary: The author explains how to calculate the physical significance of the line integral displaystyle
Line integral What is the physical significance of each line integral?
a)
∫
C
1
d
s
b)
∫
C
f
(
x
,
y
,
z
)
d
s
, where
f
(
x
,
y
,
z
)
is the density of a string of finite length.
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.
Question 2
Let F be a solenoidal vector field, suppose V × F = (-8xy + 12z², −9x² + 4y² + 9z², 6y²), and let
(P,Q,R) = V²F(.725, —.283, 1.73). Then the value of sin(2P) + sin(3Q) + sin(4R) is
-2.024
1.391
0.186
-0.994
-2.053
-0.647
-0.588
-1.851
1 pts
1 pts
Let F and G be vector fields such that ▼ × F(0, 0, 0) = (0.76, -9.78, 3.29), G(0, 0, 0) = (−3.99, 6.15, 2.94), and
G is irrotational. Then sin(5V (F × G)) at (0, 0, 0) is
Question 1
-0.246
0.072
-0.934
0.478
-0.914
-0.855
0.710
0.262
.
Chapter 15 Solutions
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