Let $\vec{a}, \vec{b}, \vec{c}$ be three vectors such that $\vec{a} \times \vec{b}=\vec{c}, \vec{b} \times \vec{c}=\vec{a}, \vec{c} \times \vec{a}=\vec{b}$ Then :

$|\vec{a}|=|\vec{b}|=|\vec{c}|$

$\vec{a} \times \vec{b}=\vec{c}, \vec{b} \times \vec{c}=\vec{a}, \vec{c} \times \vec{a}=\vec{b}$ $

$\Rightarrow \vec{c} .(\vec{a} \times \vec{b})=\vec{c} . \vec{c}, \vec{a} .(\vec{b} \times \vec{c})=\vec{a} . \vec{a}, \vec{b} .(\vec{c} \times \vec{a})=\vec{b} . \vec{b}$

$\Rightarrow[\vec{c} \vec{a} \vec{b}]=|\vec{c}|^2,[\vec{a} \vec{b} \vec{c}]=|\vec{a}|^2,[\vec{b} \vec{c} \vec{a}]=|\vec{b}|^2$

$\Rightarrow|\vec{a}|^2=|\vec{b}|^2=|\vec{c}|^2$

$\Rightarrow|\vec{a}|=|\vec{b}|=|\vec{c}|$

Hence (1) is correct answer.