Vector Algebra

Let \(a, b, c\) be three distinct real numbers, none equal to one. If the vectors \(a \hat{i}+\hat{\mathrm{j}}+\hat{\mathrm{k}}, \hat{\mathrm{i}}+b \hat{j}+\hat{\mathrm{k}}\) and \(\hat{\mathrm{i}}+\hat{\mathrm{j}}+c \hat{\mathrm{k}}\) are coplanar, then \(\frac{1}{1-a}+\frac{1}{1-b}+\frac{1}{1-c}\) is equal to :