Let a, b and c be distinct positive numbers. If the vectors a i + a j + c k, i + k and c i + c j + b k are co-planar, then c is equal to:

Let $\displaystyle \mathrm{a}, \mathrm{b}$ and c be distinct positive numbers. If the vectors $\displaystyle \mathrm{a} \hat{i}+\mathrm{a} \hat{j}+\mathrm{c} \hat{k}, \hat{i}+\hat{k}$ and $\displaystyle \mathrm{c} \hat{i}+\mathrm{c} \hat{j}+\mathrm{b} \hat{k}$ are co-planar, then c is equal to :