Question

How to find vectors of a b c if the given vector is irrotational?

Answer 1

Definition 2.4. A vector field F is called irrotational if it satisfies curl F = 0. The terminology comes from the physical interpretation of the curl. If F is the velocity field of a fluid, then curl F measures in some sense the tendency of the fluid to rotate---


Irrotational and incompressible vector fields. An irrotational vector field is a vector field where curl is equal to zero everywhere. ... Similarly, an incompressible vector field (also known as a solenoidal vector field) is one in which divergence is equal to zero everywhere.

Answer 2

If the vector field F¯¯¯¯ is irrotational, find the constant a,b,c where F¯¯¯¯=(x+2y+az)i+(bx−3y−z)j+(4x+cy+2z)k. Also show the following.