Three vectors $\overrightarrow{a},\overrightarrow{b}\text{ and }\overrightarrow{c}$ satisfy the relation $\overrightarrow{a}\cdot \overrightarrow{b}=0$ and $\overrightarrow{a}\cdot \overrightarrow{c}=0$. The vector A is parallel to

$\overrightarrow{a}\cdot \overrightarrow{b}=0\text{ i.e., }\overrightarrow{a}\text{ and }\overrightarrow{b}\text{ will be perpendicular to each other }$

$\overrightarrow{a}\cdot \overrightarrow{c}=0\text{ i.e., }\overrightarrow{a}\text{ and }\overrightarrow{c}\text{ will be perpendicular to each other }$

$\overrightarrow{b}\times \overrightarrow{c}\text{ will be a vector perpendicular to both }\overrightarrow{b}\text{ and }\overrightarrow{c}$

$\text{ So }\overrightarrow{a}\text{ is parallel to }\overrightarrow{b}\times \overrightarrow{c}\text{. }$