Answer
(a) Positive
(b) $curlF$ is zero
Work Step by Step
(a) The vector field shown is a 2D vector field of the form $F=Pi+Qj$
We know that
$divF=\frac{∂P}{∂x}+\frac{∂Q}{∂y}$
Here,
$\frac{∂P}{∂x}$ is positive, since the $x$ components of the vectors are increasing in length, as we move along the positive $x-direction$.
$\frac{∂Q}{∂y}$, is positive, since the $y$ components of the vectors are increasing in length, as we move along the positive $y-direction$.
This implies that divergence is positive.
That is, $divF=\frac{∂P}{∂x}+\frac{∂Q}{∂y}=0+(+ve)=+ve$
Hence, $divF$ is positive.
(b) The vector field shown is a 2D vector field of the form $F=Pi+Qj$
We know that
$curlF=(\frac{∂Q}{∂x}-\frac{∂P}{∂y})k$
Here $\frac{∂Q}{∂x}=0$, since the $y$ components of the vectors have same length, as we move along the positive x-direction.
$\frac{∂P}{∂y}$ is $0$, since the $x$ components of the vectors have same length as we move along the positive y-direction.
That is, $curlF=(\frac{∂Q}{∂x}-\frac{∂P}{∂y})k=(0-0)k=0$
Hence, $curlF$ is zero.
