Explanation

(c)
Let $\overrightarrow{\mathbf{OA}} = 2\widehat{\dot{\mathbf{i}}} - \widehat{\dot{\mathbf{j}}} + \widehat{\mathbf{k}},\ \overrightarrow{\mathbf{OB}} = \widehat{\dot{\mathbf{i}}} - 3\widehat{\dot{\mathbf{j}}} - 5\widehat{\mathbf{k}}$
$and\ \overrightarrow{\mathbf{OC}} = 3\widehat{\dot{\mathbf{i}}} - 4\widehat{\dot{\mathbf{j}}} - 4\widehat{\mathbf{k}}$
$\mathbf{\therefore}a = \left| \overrightarrow{\mathbf{OA}} \right| = \sqrt{6},\ b = \left| \overrightarrow{\mathbf{OB}} \right| = \sqrt{35}$
and $\overrightarrow{\mathbf{c}}\left| \overrightarrow{\mathbf{OC}} \right| = \sqrt{41}$
$\therefore\cos A = \frac{b^{2} + c^{2} + a^{2}}{2bc}$
$= \frac{\left( \sqrt{35} \right)^{2} + \left( \sqrt{41} \right)^{2} - \left( \sqrt{6} \right)^{2}}{2\sqrt{35}\ \sqrt{41}}$
$\Longrightarrow \cos{A = \sqrt{\frac{35}{41}}}$
$\Longrightarrow \ \sin^{2}{A = \frac{35}{41}}$