This operation can be rederived from the octonions in R7 using the seven-dimensional cross product.
This operation can be rederived from the octonions in R7 using the seven-dimensional cross product. A field in R3 in which this operation vanishes can be written as the gradient of some potential function, and the line integral between two points on such a field is path-independent. The surface integral of the result of this operation on a vector field is given by a line integral of the field component normal to the surface over the surface boundary, in accordance with Stokes' theorem. When this operation on a vector field equals zero, the field is said to be conservative, and the divergence applied to the result of this operation is identically zero. For 10 points, identify this vector derivative sometimes represented as the cross-product of the del symbol and a vector field, which measures instantaneous rotation.
This operation can be rederived from the octonions in R7 using the seven-dimensional cross product.
curl [accept descriptions of curl like del cross or similar before mention; prompt on "derivative"; accept cross product before "cross" is read]