question_answer

If   the   vectors,  \[\overset{\to }{\mathop{p}}\,=(a+1)\hat{i}+a\hat{j}+a\hat{k},\] \[\overset{\to }{\mathop{q}}\,=a\,\,\hat{i}+(a+1)\hat{j}+a\hat{k},\] and \[\overset{\to }{\mathop{r}}\,=a\,\,\hat{i}+a\hat{j}+(a+1)\hat{k}\,\,(a\in R)\]are coplanar and \[3{{(\overset{\to }{\mathop{p}}\,.\overset{\to }{\mathop{q}}\,)}^{2}}-\lambda {{\left| \overset{\to }{\mathop{r}}\,\times \overset{\to }{\mathop{q}}\, \right|}^{2}}=0,\]then the value of \[\lambda \] is           [JEE MAIN Held on 09-01-2020 Morning]

Answer:

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