Let three vectors $\overrightarrow a$, $\overrightarrow b$ and $\overrightarrow c$ be such that $\overrightarrow a \times \overrightarrow b = \overrightarrow c$, $\overrightarrow b \times \overrightarrow c = \overrightarrow a$ and $\left| {\overrightarrow a } \right| = 2$. Then which one of the following is not true?

(1) $$\overrightarrow a \times \left( {(\overrightarrow b + \overrightarrow c ) \times (\overrightarrow b \times \overrightarrow c )} \right)$$<br><br>$$ = \overrightarrow a ( - \overrightarrow b \times \overrightarrow c + \overrightarrow c \times \overrightarrow b ) = - 2\left( {\overrightarrow a \times (\overrightarrow b \times \overrightarrow c )} \right)$$<br><br>$= - 2(\overrightarrow a \times \overrightarrow a ) = \overrightarrow 0$<br><br>(2) Projection of $\overrightarrow a$ on $\overrightarrow b \times \overrightarrow c$<br><br>$$ = {{\overrightarrow a \,.\,(\overrightarrow b \times \overrightarrow c )} \over {\left| {\overrightarrow b \times \overrightarrow c } \right|}} = {{\overrightarrow a .\overrightarrow a } \over {\left| {\overrightarrow a } \right|}} = \left| {\overrightarrow a } \right| = 2$$<br><br>(3) $$\left[ {\overrightarrow a \overrightarrow b \overrightarrow c } \right] + \left[ {\overrightarrow c \overrightarrow a \overrightarrow b } \right] = 2\left[ {\overrightarrow a \overrightarrow b \overrightarrow c } \right] = 2\overrightarrow a .(\overrightarrow b \times \overrightarrow c )$$<br><br>$$ = 2\overrightarrow a .\overrightarrow a = 2{\left| {\overrightarrow a } \right|^2} = 8$$<br><br>(4) $\overrightarrow a \times \overrightarrow b = \overrightarrow c$ and $\overrightarrow b \times \overrightarrow c = \overrightarrow a$<br><br>$\Rightarrow \overrightarrow a ,\overrightarrow b ,\overrightarrow c$ are mutually $\bot$ vectors.<br><br>$\therefore$ $$\left| {\overrightarrow a \times \overrightarrow b } \right| = \left| {\overrightarrow c } \right| \Rightarrow \left| {\overrightarrow a } \right|\left| {\overrightarrow b } \right| = \left| {\overrightarrow c } \right| \Rightarrow \left| {\overrightarrow b } \right| = {{\left| {\overrightarrow c } \right|} \over 2}$$<br><br>Also, $$\left| {\overrightarrow b \times \overrightarrow c } \right| = \left| {\overrightarrow a } \right| \Rightarrow \left| {\overrightarrow b } \right|\left| {\overrightarrow c } \right| = 2 \Rightarrow \left| {\overrightarrow c } \right| = 2$$ &amp; $\left| {\overrightarrow b } \right| = 1$<br><br>$${\left| {3\overrightarrow a + \overrightarrow b - 2\overrightarrow c } \right|^2} = (3\overrightarrow a + \overrightarrow b - 2\overrightarrow c ).(3\overrightarrow a + \overrightarrow b - 2\overrightarrow c )$$<br><br>$$ = 9{\left| {\overrightarrow a } \right|^2} + {\left| {\overrightarrow b } \right|^2} + 4{\left| {\overrightarrow c } \right|^2}$$<br><br>$= (9 \times 4) + 1 + (4 \times 4)$<br><br>$= 36 + 1 + 16 = 53$