Three vectors $\overrightarrow{\mathrm{p}}, \overrightarrow{\mathrm{q}}$, and $\overrightarrow{\mathrm{r}}$ are given as
\[
\begin{array}{c}
\overrightarrow{\mathrm{p}}=\hat{\imath}+\hat{\jmath}+\hat{k} \\
\overrightarrow{\mathrm{q}}=\hat{\imath}+2 \hat{\jmath}+3 \hat{k} \\
\overrightarrow{\mathrm{r}}=2 \hat{\imath}+3 \hat{\jmath}+4 \hat{k}
\end{array}
\]
Which of the following is/are CORRECT?
- $\vec{p} \times(\vec{q} \times \vec{r})+\vec{q} \times(\vec{r} \times \vec{p})+\vec{r} \times(\vec{p} \times \vec{q})=\overrightarrow{0}$
- $\overrightarrow{\mathrm{p}} \times(\overrightarrow{\mathrm{q}} \times \overrightarrow{\mathrm{r}})=(\overrightarrow{\mathrm{p}} \bullet \overrightarrow{\mathrm{r}}) \overrightarrow{\mathrm{q}}-(\overrightarrow{\mathrm{p}} \bullet \overrightarrow{\mathrm{q}}) \overrightarrow{\mathrm{r}}$
- $\vec{p} \times(\vec{q} \times \vec{r})=(\vec{p} \times \vec{q}) \times \vec{r}$
- $\overrightarrow{\mathrm{r}} \bullet(\overrightarrow{\mathrm{p}} \times \overrightarrow{\mathrm{q}})=(\overrightarrow{\mathrm{q}} \times \overrightarrow{\mathrm{p}}) \bullet \overrightarrow{\mathrm{r}}$