Explanation

(a)
Now, $\widehat{\dot{\mathbf{i}}} \times \left( \widehat{\dot{\mathbf{j}}} \times \widehat{\mathbf{k}} \right) = \widehat{\dot{\mathbf{i}}} \times \widehat{\dot{\mathbf{i}}} = \overrightarrow{\mathbf{0}}$
$\widehat{\dot{\mathbf{j}}} \times \left( \widehat{\mathbf{k}} \times \widehat{\dot{\mathbf{i}}} \right) = \widehat{\dot{\mathbf{j}}} \times \widehat{\dot{\mathbf{j}}} = \overrightarrow{\mathbf{0}}$
$and\ \widehat{\mathbf{k}} \times \left( \widehat{\dot{\mathbf{i}}} \times \widehat{\dot{\mathbf{j}}} \right)\widehat{\mathbf{k}} \times \widehat{\mathbf{k}} = \overrightarrow{\mathbf{0}}$
$\therefore\ \widehat{\dot{\mathbf{i}}} \times \left( \widehat{\dot{\mathbf{j}}} \times \widehat{\mathbf{k}} \right) + \widehat{\dot{\mathbf{j}}} \times \left( \widehat{\mathbf{k}} \times \widehat{\dot{\mathbf{i}}} \right) + \widehat{\mathbf{k}} \times \left( \widehat{\dot{\mathbf{i}}} \times \widehat{\dot{\mathbf{j}}} \right) = \overrightarrow{\mathbf{0}}$