Let three vectors $\overline{a},\overline{b},\overline{c}$ be such that $\overline{a}\times \overline{b}=\overline{c}, \overline{b}\times \overline{c}=\overline{a}$ and $\left|\overline{a}\right|=2$ Then which of the following is NOT TRUE?

$\overline{a}\times \overline{b}=\overline{c} \Rightarrow \overline{c}$  is perpendicular to $\overline{a}=\overline{b}$
$\overline{b}\times \overline{c}=\overline{a}\Rightarrow \overline{a}$  is perpendicular to  $\overline{b}=\overline{c}$
So $\overline{a},\overline{b},\overline{c}$ are mutually perpendicular 
$$\begin{gathered} \overline{a}\times \overline{b}=\overline{c}\Rightarrow \left|a\right|\left|b\right|=\left|\overline{c}\right|\Rightarrow \left|\overline{b}\right|=\frac{\left|\overline{c}\right|}{2} \\ \overline{b}\times \overline{c}=\overline{a}\Rightarrow \left|\overline{b}\right|\left|\overline{c}\right|=\left|\overline{a}\right|\Rightarrow \left|c\right|=2 \\ \left|\overline{b}\right|=1 \end{gathered}$$

 $1) \left[\overline{a}\overline{b}\overline{c}\right]+\left[\overline{c}\overline{a}\overline{b}\right]=2\left[\overline{a}\overline{b}\overline{c}\right]=2\left|a\right|\left|b\right|\left|c\right|=8$

2) $\overline{a}$ is parallel to $\overline{b}\times \overline{c}$  
So Projection of $\overline{a}$ on $\overline{b}\times \overline{c}=\frac{\overline{a}(\overline{b}\times \overline{c})}{|\overline{b}\times \overline{c}|}=\frac{\left[abc\right]}{\left|b\right|\left|c\right|}=\frac{4}{2}=2$
3) ${|3\overline{a}+\overline{b}-2\overline{c}|}^2=9{\left|a\right|}^2+{\left|\overline{b}\right|}^2+4{\left|c\right|}^2=53$