Let the vectors \( (2+a+b) \hat{i}+(a+2 b+c) \hat{j}-(b+c) \hat{k}, \ (1+b) \hat{i}+2 b j-b \hat{k}\) and \((2+b) \hat{i…

Let the vectors \( (2+a+b) \hat{i}+(a+2 b+c) \hat{j}-(b+c) \hat{k}, \ (1+b) \hat{i}+2 b j-b \hat{k}\) and \((2+b) \hat{i}+2 b \hat{j}+(1-b) \hat{k}, a, b, c \in R\) be co-planar. Then which of the following is true?