$${\overrightarrow r _1} = \widehat i - 8\widehat j + 4\widehat k$$

$${\overrightarrow r _2} = \widehat i + 2\widehat j + 6\widehat k$$

$$\overrightarrow a = 2\widehat i - 7\widehat j + 5\widehat k$$

$$\overrightarrow b = 2\widehat i + \widehat j - 3\widehat k$$

S.D. $$ = {{\left| {\matrix{ {{{\overrightarrow r }_1} - {{\overrightarrow r }_2}} & {\matrix{ {\overrightarrow a } & {\overrightarrow b } \cr } } \cr } } \right|} \over {\left| {\overrightarrow a \times \overrightarrow b } \right|}}$$

$$\left[ {\matrix{ {{{\overrightarrow r }_1} - {{\overrightarrow r }_2}} & {\matrix{ {\overrightarrow a } & {\overrightarrow b } \cr } } \cr } } \right] = \left| {\matrix{ 0 & { - 10} & { - 2} \cr 2 & { - 7} & 5 \cr 2 & 1 & { - 3} \cr } } \right|$$

$$\therefore$$ $$10( - 16) - 2(16) = - 192$$

$$\left| {\left[ {\matrix{ {{{\overrightarrow r }_1} - {{\overrightarrow r }_2}} & {\matrix{ {\overrightarrow a } & {\overrightarrow b } \cr } } \cr } } \right]} \right| = 192$$

$$\overrightarrow a \times \overrightarrow b = \left| {\matrix{ {\widehat i} & {\widehat j} & {\widehat k} \cr 2 & { - 7} & 5 \cr 2 & 1 & { - 3} \cr } } \right| = 16\widehat i + 16\widehat j + 16\widehat k$$

$$\overrightarrow a \times \overrightarrow b = 16\sqrt 3 $$

S.D. $$ = {{192} \over {16\sqrt 3 }} = 4\sqrt 3 $$