Geography Reference
In-Depth Information
APPENDIX C
Vector Analysis
C.1
VECTOR IDENTITIES
The following formulas may be shown to hold where is an arbitrary scalar
and
A
and
B
are arbitrary vectors.
∇
×
∇
=
0
∇·
(
A
)
=
∇·
(
A
)
+
A
·∇
∇
×
(
A
)
=
∇
×
A
+
(
∇
×
A
)
∇·
∇
×
=
(
A
)
0
1
2
∇
(
A
·∇
)
A
=
(
A
·
A
)
−
A
×
(
∇
×
A
)
∇
×
(
A
×
B
)
=
A
(
∇·
B
)
−
B
(
∇·
A
)
−
(
A
·∇
)
B
+
(
B
·∇
)
A
A
×
(
B
×
C
)
=
(
A
·
C
)
B
−
(
A
·
B
)
C
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