Explanation

(a)
$\overrightarrow{\mathbf{PQ}} = 6\widehat{\dot{\mathbf{i}}} + \widehat{\dot{\mathbf{j}}}$l
$\overrightarrow{\mathbf{QR}} = - \widehat{\dot{\mathbf{i}}} + 3\widehat{\dot{\mathbf{j}}}$
$\overrightarrow{\mathbf{RS}} = - 6\widehat{\dot{\mathbf{i}}} - \widehat{\dot{\mathbf{j}}}$
$\overrightarrow{\mathbf{SP}} = \widehat{\dot{\mathbf{i}}} - 3\widehat{\dot{\mathbf{j}}}$
$\left| \overrightarrow{\mathbf{PQ}} \right| = \sqrt{37} = \left| \overrightarrow{\mathbf{RS}} \right|$
$\left| \overrightarrow{\mathbf{QR}} \right| = \sqrt{10} = \left| \overrightarrow{\mathbf{SP}} \right|$
$\overrightarrow{\mathbf{PQ}} \bullet \overrightarrow{\mathbf{QR}} = - 6 + 3 = - 3 \neq 0$
$\overrightarrow{\mathbf{PQ}} =$ is not parallel to $\overrightarrow{\mathbf{RS}}$ and their magnitude are equal.
$\Longrightarrow$ Quadrilateral $PQRS$ must be a parallelogram, which is neither a rhombus nor a rectangle.