Value of $[\vec{a} \times \vec{b}, \vec{a} \times \vec{c}, \vec{d}]$ is always equal to:

$(\vec{a}. \vec{d})[\vec{a} \vec{b} \vec{c}]$

${[\vec{a} \times \vec{b}, \vec{a} \times \vec{c}, \vec{d}]}$

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

$=(\vec{a} \times \vec{b}) .((\vec{a} . \vec{d}) \vec{c}-(\vec{c} . \vec{d}) \vec{a})$

$=(\vec{a} . \vec{d})[\vec{a} \vec{b} \vec{c}]$

Hence (1) is correct answer.