The velocity field on an incompressible flow is given by
$$V = \left( {{a_1}x + {a_2}y + {a_3}z} \right)i + \left( {{b_1}x + {b_2}y + {b_3}z} \right)j$$ $$$ + \left( {{c_1}x + {c_2}y + {c_3}z} \right)k,$$$

Where $${a_1} = 2$$ and $${c_3} = - 4.$$ The value of $${b_2}$$ is _____________.

Consider the following statements regarding streamline(s):
(i) It is a continuous line such that the tangent at any point on it shows the velocity vector at that point
(ii) There is no flow across streamlines
(iii) $${{dx} \over u} = {{dy} \over v} = {{dz} \over w}$$ is the differential equation of a streamline, where $$u,v$$ and $$w$$ are velocities in directions $$x,y$$ and $$z,$$ respectively
In an unsteady flow, the path of a particle is a streamline

Which one of the following combinations of the statements is true?

Consider a velocity field $$\overrightarrow V = K\left( {y\widehat i + x\widehat k} \right),$$ where $$K$$ is a constant. The vorticity, $${\Omega _z},$$ is

Velocity vector of a flow fields is given as $$\overrightarrow V = 2xy\widehat i - {x^2}z\widehat j.$$ The vorticity vector at $$(1,1,1)$$ is