EXAMPLE 5 Show that the vector field F(x, y, z) = xz'i + x'yz°j - yk can't be written as the curl of another vector field, that is, F * curl G. SOLUTION As we showed in this example, it can be shown...

Extracted text: EXAMPLE 5 Show that the vector field F(x, y, z) = xz'i + x'yz°j - yk can't be written as the curl of another vector field, that is, F * curl G. SOLUTION As we showed in this example, it can be shown that div F = and therefore div F = v 0. If it were true that F = curl G, then this theorem would give div F = div curl G = 0 which contradicts div F = v0. Therefore F is not the curl of another vector field.