$${{x - {1 \over 8}} \over {{1 \over 8}}} = {y \over { - {1 \over {4\sqrt 2 }}}} = {z \over 0}\,\,\,\,\,\,\,\,\,\,\,\,\,$$ ______L₁

or $${{x - {1 \over 8}} \over 1} = {y \over { - \sqrt 2 }} = {z \over 0}$$ ..... (i)

Equation of L₂

$${{x + {1 \over 8}} \over { - 6\sqrt 3 }} = {y \over 0} = {z \over 8}$$ ...... (ii)

$$d = \left| {{{(\overrightarrow c - \overrightarrow a )\,.\,(\overrightarrow b \times \overrightarrow d )} \over {\left| {\overrightarrow b \times \overrightarrow d } \right|}}} \right|$$

$$ = {{\left( {{1 \over 4}\widehat i} \right)\,.\,\left( {4\sqrt 2 \widehat i + 4\widehat j + 3\sqrt 6 \widehat k} \right)} \over {\sqrt {{{\left( {4\sqrt 2 } \right)}^2} + {4^2} + {{\left( {3\sqrt 6 } \right)}^2}} }}$$

$$ = {{\sqrt 2 } \over {\sqrt {32 + 16 + 54} }} = {1 \over {\sqrt {51} }}$$

$${d^{ - 2}} = 51$$