If F(x,y,z)𝐹(𝑥,𝑦,𝑧) is a vector field such that curl(F)≠0(𝐹)≠0 then:a.there will be a scalar field f𝑓 such that F=∇(f)𝐹=∇(𝑓).b.F𝐹 is a conservative vector field.c.F𝐹 is irrotational.d.none of the choices are true.

A vector field F⃗ 𝐹→ is called solenoidal ifa.div(curl(F⃗ ))=0𝑑𝑖𝑣(𝑐𝑢𝑟𝑙(𝐹→))=0b.curl(F⃗ )=0𝑐𝑢𝑟𝑙(𝐹→)=0c.div(F⃗ )=0𝑑𝑖𝑣(𝐹→)=0d.None of these

Which of the following statements are true? (one or more than one may be correct)The arc length parameter is a scalarThe arc length parameter is a vectorThe curl of a field is a scalar.The curl of a field is a vector.Greens theorem links the circulation to the kth component of the curlGreens theorem links the circulation to the divergence of the field

How to find curl of a vector field?

Which of the following statements about line integrals are true? (one or more than one maybe correct). Line integrals of conservative fields over closed loops are zero.Line integrals of conservative fields over closed loops are non-zero.If curl of the field is a zero vector, the field is non-conservative.Line integrals of conservative fields are path dependent.Line integrals of conservative fields are path independent.

Explain irrotational or solenoidal fields. Verify whether given vector field A isirrotational or solenoidal.A = (yz) ax + (zx) av + (xy) az