Use the result of Exercise 43(b) to show that if F is a vector field of the form F = f r r and if div F = 0 , then F is an inverse-square field. [ Suggestion : Let r = r and multiply 3 f ( r ) + r f ′ ( r ) = 0 through by r 2 . Then write the result as a derivative of a product.]
Use the result of Exercise 43(b) to show that if F is a vector field of the form F = f r r and if div F = 0 , then F is an inverse-square field. [ Suggestion : Let r = r and multiply 3 f ( r ) + r f ′ ( r ) = 0 through by r 2 . Then write the result as a derivative of a product.]
Use the result of Exercise 43(b) to show that if F is a vector field of the form
F
=
f
r
r
and if div
F
=
0
,
then F is an inverse-square field. [Suggestion:
Let
r
=
r
and multiply
3
f
(
r
)
+
r
f
′
(
r
)
=
0
through by
r
2
.
Then write the result as a derivative of a product.]
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.
Precalculus: Mathematics for Calculus (Standalone Book)
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