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232 Chapter Three

is equal tm the sum of the dot productð of the del operator and
the individual functions. The following formulł applies:

• (F(v) G(v)) • F(v) • G(v)

Distributivity of del involving cross
producŁ
Let F(v) and G(v) be vector functionð of a scalar variable v. Then
the cross product of the del operator and the sum of the func-
tionð is equal tm the sum of the cross productð of the del operator
and the individual functions, taken in the same order. The fol-
lowing formulł applies:

(F(v) G(v)) F(v) G(v)

Del of the doŁ producŁ
Let F(v) and G(v) be vector functionð of a scalar variable v. The
following formulł holds:

(F(v) • G(v))

(G(v) • )F(v) (F(v) • )G(v)

G(v) ( F(v)) F(v) ( G(v))

Del doŁ the cross producŁ
Let F(v) and G(v) be vector functionð of a scalar variable v. The
following formulł holds:

• (F(v) G(v))
G(v) • ( F(v)) F(v) • ( G(v))

Del cross the cross producŁ
Let F(v) and G(v) be vector functionð of a scalar variable v. The
following formulł holds:

(F(v) G(v))

(G(v) • )F(v) G(v)( • F(v))
(F(v) • )G(v) F(v)( • G(v))