For $a \in R$, if the vectors $\bar{p}=(a+1) \bar{i}+a \bar{j}+a \bar{k}, \overline{\mathrm{q}}=\mathrm{a} \overline{\mathrm{i}}+(\mathrm{a}+1) \overline{\mathrm{j}}+\mathrm{a} \overline{\mathrm{k}}$ and $\bar{r}=a \bar{i}+a \bar{j}+(a+1) \bar{k}$ are coplanar and $3(\bar{p} \cdot \bar{q})^2-\lambda|\bar{r} \times \bar{q}|^2=0$, then the value of $\lambda$ is

• A

  $\frac{2}{3}$
• B

  $\frac{3}{2}$
• C

  2
• Correct answer
  D

  1

Hence, the correct answer is option: 'D'.