Answer:
(a) curl f - meaningless
(b) grad f -Δf- vector field
(c) div F - scalar field
(d) curl( grad f )curl (Δf)- vector field (e) grad F -ΔF- meaningless
(f) grad( div F )-Δ(divF) - vector field
(g) div( grad f ) - div(Δf)- scalar field
(h) grad ( div f ) -Δ(div f)-meaningless
(i) curl ( curl F ) - vector field
(j) div( div F ) - meaningless
(k) ( grad f ) x ( div F ) -(Δf) x (divF)-meaningless
(l) div( curl( grad f )) -div(curl(Δf))-scalar field
Step-by-step explanation:
(a) curl f - meaningless; a curl can only be taken of a vector field
(b) grad f - vector field; a gradient results in a vector field
(c) div F - scalar field; a divergence results in a scalar field
(d) curl( grad f ) - vector field; the curl of a vector field results in a vector field
(e) grad F - meaningless; a gradient can only be taken of a scalar field
(f) grad( div F ) -vector field ; the gradient of a scalar field is a vector field
(g) div( grad f ) - scalar field; the divergence of a vector field is a scalar field
(h) grad ( div f ) - meaningless; the divergence of a scalar field can not be taken
(i) curl ( curl F ) - vector field; the curl of a vector field is a vector field
(j) div( div F ) - meaningless; the divergence of a scalar field can not be taken
(k) ( grad f ) x ( div F ) - meaningless; a vector and scalar field cannon be crossed
(l) div( curl( grad f )) - scalar field; the divergence of a vector field is a scalar field
