Let Is $\vec {F }$ A Divergence Free Vector Field

question 17

Short Answer

Let $\vec { F } = - \frac { x } { \left( x ^ { 2 } + 4 y ^ { 2 } + 3 z ^ { 2 } \right) ^ { 3 / 2 } } \vec { i } - \frac { y } { \left( x ^ { 2 } + 4 y ^ { 2 } + 3 z ^ { 2 } \right) ^ { 3 / 2 } } \vec { j } - \frac { z } { \left( x ^ { 2 } + 4 y ^ { 2 } + 3 z ^ { 2 } \right) ^ { 3 / 2 } } \vec { k }$ Is $\vec {F }$ a divergence free vector field?

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