Explanation

(a)
Let $\overrightarrow{\mathbf{a}} = (2,1, - 1)$,$\ \overrightarrow{\mathbf{b}} = (1, - 1,0)$and $\overrightarrow{\mathbf{c}} = (5, - 1,1)$
$\therefore\ \overrightarrow{\mathbf{a}} + \overrightarrow{\mathbf{b}} - \overrightarrow{\mathbf{c}} = (2 + 1 - 5)\widehat{\dot{\mathbf{i}}} + (1 - 1 + 1)\widehat{\dot{\mathbf{j}}} + ( - 1 + 0 - 1)\widehat{\dot{\mathbf{k}}}$
$= - \left( 2\widehat{\dot{\mathbf{i}}} - \widehat{\dot{\mathbf{j}}} + 2\widehat{\dot{\mathbf{k}}} \right)$
$\therefore$ Unit vector of
$\left( \overrightarrow{\mathbf{a}} + \overrightarrow{\mathbf{b}} - \overrightarrow{\mathbf{c}} \right) = - \frac{(2\widehat{\dot{\mathbf{i}}} - \widehat{\dot{\mathbf{j}}} + 2\widehat{\dot{\mathbf{k}}})}{3}$
$\therefore\ \$Required unit vector of
$\left( \overrightarrow{\mathbf{a}} + \overrightarrow{\mathbf{b}} - \overrightarrow{\mathbf{c}} \right) = \frac{(2\widehat{\dot{\mathbf{i}}} - \widehat{\dot{\mathbf{j}}} + 2\widehat{\dot{\mathbf{k}}})}{3}$