Let a, b, c be three distinct real numbers, none equal to one. If the vectors a i + j + k, i +b j + k and i + j +c k are coplanar, then…

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