If the vectors,

If the vectors, $\vec{p}=(a+1) \hat{i}+a \hat{j}+a \hat{k}$,

$\overrightarrow{\mathrm{q}}=a \hat{\mathrm{i}}+(\mathrm{a}+1) \hat{\mathrm{j}}+\mathrm{a} \hat{\mathrm{k}}$ and

$\overrightarrow{\mathrm{r}}=a \hat{\mathrm{i}}+\mathrm{aj}+(\mathrm{a}+1) \hat{\mathrm{k}} \quad(\mathrm{a} \in \mathrm{R}) \quad$ are coplanar

and $3(\overrightarrow{\mathrm{p}} \cdot \overrightarrow{\mathrm{q}})^{2}-\lambda|\overrightarrow{\mathrm{r}} \times \overrightarrow{\mathrm{q}}|^{2}=0$, then the value of $\lambda$ is_________________.