Consider a velocity vector, $\vec{V}$ in ( $\mathrm{x}, \mathrm{y}, \mathrm{z}$ ) coordinates given below. Pick one or more CORRECT statement(s) from the choices given below:

$$ \vec{V}=u \vec{x}+v \vec{y} $$

Let 𝜙 be a scalar field, and 𝒖 be a vector field. Which of the following identities is true for div(𝜙𝒖)?

The divergence of the vector field $$\,V = {x^2}i + 2{y^3}j + {z^4}k\,\,$$ at $$x=1, y=2, z=3$$ is ________.

For the parallelogram $$OPQR$$ shown in the sketch. $$\,\overrightarrow {OP} = a\widehat i + b\widehat j$$ and $$\,\overrightarrow {OR} = c\widehat i + d\widehat j.\,\,$$ The area of the parallelogram is