If $\overrightarrow{a},\overrightarrow{b}\text{ and }\overrightarrow{c}$ are non-zero coplanar vectors, such that $\overrightarrow{a}\cdot \overrightarrow{b}=\overrightarrow{b}\cdot \overrightarrow{c}=0\text{. If }\left|\overrightarrow{a}\right|=1\text{ unit and }\left|\overrightarrow{c}\right|=6\text{ units. The value }$$\text{ of }|\overrightarrow{a}\cdot \overrightarrow{c}|.\text{ is }$_________

$\because \overrightarrow{a}\cdot \overrightarrow{b}=\overrightarrow{b}\cdot \overrightarrow{c}=0$

It means $\overrightarrow{a}$ and $\overrightarrow{b}$ are perpendicular to each other. Similarly, $\overrightarrow{b}$ and $\overrightarrow{c}$ are perpendicular to each other. So, we can say that $\overrightarrow{a}$ and $\overrightarrow{c}$ are parallel to each other. 

$\therefore \overrightarrow{a}\cdot \overrightarrow{c}=|a\parallel c|\cos 0^{\circ }=1\times 6=6\text{ units }$