Let \(a, b, c\) be three distinct real numbers, none equal to one. If the vectors \(a \hat{i}+\hat{j}+\hat{k}, \hat{i}+b…

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

[JEE Main 2023, 12 Apr (Shift 1)]