If $\hat{a}, \hat{b}, \hat{c}$ are three non-coplanar unit vectors, then $[\hat{a} \vec{p} \vec{q}] \hat{a}+\mid \hat{b} \vec{p} \vec{q}] \hat{b}+[\hat{c} \vec{p} \vec{q}] \hat{c}$ is equal to

$\vec{p} \times \vec{q}$

$[\hat{a} \vec{p} \vec{q}]=$ projection of $\vec{p} \times \vec{q}$ in the direction of $\hat{a}$.

Hence the given vector is $\vec{p} \times \vec{q}$

Hence (4) is correct answer.