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Home Vector Calculus Independence of Path Theorem 1 (Three Variables)
 
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Theorem 1 (Three Variables)

Theorems 1 and 2 also hold for three variables. For three variables a vector field has the form

F(x, y, z) = P(x, y, z)i + Q(x, y, z)j + R(x, y, z)k.

Theorem 1 for three variables reads as follows.

THEOREM 1 (Three Variables)

A vector field Pi + Qj + Rk has a potential function if and only if

13_vector_calculus-162.gif

Theorem 2 is modified in the same way.
Home Vector Calculus Independence of Path Theorem 1 (Three Variables)

Last Update: 2006-11-22