Let the vectors (2+ a + b ) i +( a +2 b + c ) j -( b + c ) k, (1+ b ) i +2 b j - b k and (2+ b ) i +2 b j +(1- b ) k, a, b, c ∈ R be co-planar. Then…

Let the vectors $$\begin{aligned} & (2+\mathrm{a}+\mathrm{b}) \hat{i}+(\mathrm{a}+2 \mathrm{~b}+\mathrm{c}) \hat{j}-(\mathrm{b}+\mathrm{c}) \hat{k}, \\ & (1+\mathrm{b}) \hat{i}+2 \mathrm{~b} \hat{j}-\mathrm{b} \hat{k} \text { and }(2+\mathrm{b}) \hat{i}+2 \mathrm{~b} \hat{j}+(1-\mathrm{b}) \hat{k}, \mathrm{a}, \mathrm{~b}, \mathrm{c} \in \mathbf{R} \end{aligned} $$ be co-planar. Then which of the following is true ?