Explanation

(d)
Given lines can be rewritten as
$\overrightarrow{\mathbf{r}} = 2\widehat{\dot{\mathbf{i}}} + \widehat{\dot{\mathbf{j}}} + 2\widehat{\mathbf{k}} + t( - 3\widehat{\dot{\mathbf{i}}} + 2\widehat{\dot{\mathbf{j}}} + 6\widehat{\mathbf{k}})$
$and\ \overrightarrow{\mathbf{r}} = \widehat{\dot{\mathbf{i}}} + 2\widehat{\dot{\mathbf{j}}} - \widehat{\mathbf{k}} + s\left( 4\widehat{\dot{\mathbf{i}}} - \widehat{\dot{\mathbf{j}}} + 8\widehat{\mathbf{k}} \right)$
here, $a_{1} = - 3,b_{1} = 2,c_{1} = 6$
and $a_{2} = 4,b_{2} = - 1,c_{2} = 8$
$\therefore\cos\theta = \frac{a_{1}a_{2} + b_{1}b_{2} + c_{1}c_{2}}{\sqrt{a_{1}^{2} + b_{1}^{2} + c_{1}^{2}}\sqrt{a_{2}^{2} + b_{2}^{2} + c_{2}^{2}}}$
$= \frac{- 3 \times 4 + 2 \times ( - 1) + 6 \times 8}{\sqrt{9 + 4 + 36}\ \sqrt{16 + 1 + 64}} = \frac{34}{7 \times 9}$
$\Longrightarrow \ \theta = \cos^{- 1}\left( \frac{34}{63} \right)$