Determine whether the vector field is conservative. If it is, find a potential function for the vector field. $$\overrightarrow { \mathbf { F } } ( x , y , z ) = 7 x ^ { 6 } y ^ { 8 } z ^ { 9 } \hat { \mathbf { i } } + 8 x ^ { 7 } y ^ { 7 } z ^ { 9 } \hat { \mathbf { j } } + 9 x ^ { 7 } y ^ { 8 } z ^ { 8 } \hat { \mathbf { k } }$$
A) conservative with potential function $f ( x , y , z ) = x ^ { 8 } y ^ { 8 } z ^ { 8 }$
B) conservative with potential function $f ( x , y , z ) = x ^ { 7 } y ^ { 8 } z ^ { 9 }$
C) conservative with potential function $f ( x , y , z ) = x ^ { 9 } y ^ { 8 } z ^ { 7 }$
D) conservative with potential function $f ( x , y , z ) = x ^ { 9 } y ^ { 9 } z ^ { 9 }$
E) not conservative

Question

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The Answer of Determine whether the vector field is conservative. If it is, find a potential function for the vector field. $$\overrightarrow { \mathbf { F } } ( x , y , z ) = 7 x ^ { 6 } y ^ { 8 } z ^ { 9 } \hat { \mathbf { i } } + 8 x ^ { 7 } y ^ { 7 } z ^ { 9 } \hat { \mathbf { j } } + 9 x ^ { 7 } y ^ { 8 } z ^ { 8 } \hat { \mathbf { k } }$$
A) conservative with potential function $f ( x , y , z ) = x ^ { 8 } y ^ { 8 } z ^ { 8 }$
B) conservative with potential function $f ( x , y , z ) = x ^ { 7 } y ^ { 8 } z ^ { 9 }$
C) conservative with potential function $f ( x , y , z ) = x ^ { 9 } y ^ { 8 } z ^ { 7 }$
D) conservative with potential function $f ( x , y , z ) = x ^ { 9 } y ^ { 9 } z ^ { 9 }$
E) not conservative

Determine Whether the Vector Field Is Conservative A) Conservative with Potential Function