Explanation

(d)
Let $\overrightarrow{\mathbf{P}} = \widehat{\dot{\mathbf{i}}} + \widehat{\dot{\mathbf{j}}} - \widehat{\mathbf{k}},\ \ \overrightarrow{\mathbf{Q}} = 2\widehat{\dot{\mathbf{i}}} + 3\widehat{\dot{\mathbf{j}}}\ ,\ \ \ \overrightarrow{\mathbf{R}} = 5\widehat{\dot{\mathbf{j}}} - 2\widehat{\mathbf{k}}$
and $\overrightarrow{\mathbf{S}} = - \widehat{\dot{\mathbf{j}}} + \widehat{\mathbf{k}}$
$\therefore\ \overrightarrow{\mathbf{PQ}} = \widehat{\dot{\mathbf{i}}} + 2\widehat{\dot{\mathbf{j}}} + \widehat{\mathbf{k}}$
$\Longrightarrow \left| \overrightarrow{\mathbf{PQ}} \right| = \sqrt{6}$
$\overrightarrow{\mathbf{QR}} = - 2\widehat{\dot{\mathbf{i}}} + 2\widehat{\dot{\mathbf{j}}} - 2\widehat{\mathbf{k}}$
$\Longrightarrow \left| \overrightarrow{\mathbf{QR}} \right| = \sqrt{12}$
and $\overrightarrow{\mathbf{RS}} = - 6\widehat{\dot{\mathbf{j}}} + 3\widehat{\mathbf{k}}$
$\Longrightarrow \left| \overrightarrow{\mathbf{RS}} \right| = \sqrt{45}$
and $\overrightarrow{\mathbf{SP}} = \widehat{\dot{\mathbf{i}}} + 2\widehat{\dot{\mathbf{j}}} - 2\widehat{\mathbf{k}}\ \ \ \ \Longrightarrow \left| \overrightarrow{\mathbf{SP}} \right| = 3$
Which are not satisfied the conditions of any of the following. Trapezium, rectangle and parallelogram.