If the vectors, p =( a +1) i + a j + a k, q = a i +( a +1) j + a k and r = a i + a j +( a +1) k ( a ∈ R ) are coplanar and 3( p · q )^2-λ| r × q…

If the vectors, $\displaystyle \overrightarrow{\mathrm{p}}=(\mathrm{a}+1) \hat{i}+\mathrm{a} \hat{j}+\mathrm{a} \hat{k}$, $$\begin{aligned} & \overrightarrow{\mathrm{q}}=\mathrm{a} \hat{i}+(\mathrm{a}+1) \hat{j}+\mathrm{a} \hat{k} \quad \text { and } \\ & \overrightarrow{\mathrm{r}}=\mathrm{a} \hat{i}+\mathrm{a} \hat{j}+(\mathrm{a}+1) \hat{k} \quad(\mathrm{a} \in \mathrm{R}) \text { are } \end{aligned} $$ coplanar and $\displaystyle 3(\overrightarrow{\mathrm{p}} \cdot \overrightarrow{\mathrm{q}})^2-\lambda|\overrightarrow{\mathrm{r}} \times \overrightarrow{\mathrm{q}}|^2=0$, then the value of $\displaystyle \lambda$ is \_\_\_\_.