Please be clear and type the answer Granted sufficient diffe

Granted sufficient differentiability, which of the following expressions make sense? f curl v, v curl f, u times v, u times v times w, f middot v, f middot (v times w), u middot (v times w), v times curl v, div (fv), curl (fv), and curl (f middot v).

Solution

Here the function f is scalar funtion and u,v and w be the vectors

so the expressions

(1) f curlv is meaning full because curlv is defined and f curlv means scalar function multiplication of curlv

(2) v curl f is not defined because curl f is not not defined

(3) u x v is vector product it is defined

(4) u x v x w   is defined this is triple vector product

(5) f.v is not possible because scalar product is possible b/w two vectors.

(6) f.(v x w) is not possible this is also scalar product b/w scalar and vector

(7) u.(v x w) possible because v x w is vector

(8) v x curlv is possible

(9) div(fv) possible

(10) curl(fv) is defined

(11) curl(.v) is not defined