$4$au$($x$,$y$,$z$),$v$($x$,$y$,$z$)$ and w$($x$,$y$,$z$)$ be functionally related through the

equation F$($u$,$v$,$w$)=0$ is $[$vec$($grad$)$uvec$($grad$)$vvec$($grad$)$w$]=0,$ where vec$($a$)$vec$($b$)$vec$($c$)$ is the scalar

triple product of the vectors vec$($a$),$vec$($b$)$ and vec$($c$).$

solve it in detailed.