If the lines $\vec{r}=\vec{a}+t(\vec{b} \times \vec{c})$ and $\vec{r}=\vec{b}+s(\vec{c} \times \vec{a})$ intersect (t and s are scalars) then

$\vec{a} . \vec{c}=\vec{b} . \vec{c}$

For the point of intersection of the lines

$\vec{a}+t(\vec{b} \times \vec{c})=\vec{b}+s(\vec{c} \times \vec{a}) \Rightarrow \vec{a} \vec{c}+t(\vec{b} \times \vec{c}) \vec{c}=\vec{b} .\vec{c}+s(\vec{c} \times \vec{a}) \vec{c}$

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

Hence (2) is correct answer.