Let a = i -2 j + k and b = i - j + k be two vectors. If c is a vector such that b × c = b × a and c · a =0, then c · b is equal to:

Let $\displaystyle \vec{a}=\hat{i}-2 \hat{j}+\hat{k} \quad$ and $\displaystyle \overrightarrow{\mathrm{b}}=\hat{i}-\hat{j}+\hat{k}$ be two vectors. If $\displaystyle \overrightarrow{\mathrm{c}}$ is a vector such that $\displaystyle \vec{b} \times \vec{c}=\vec{b} \times \vec{a}$ and $\displaystyle \vec{c} \cdot \vec{a}=0$, then $\displaystyle \vec{c} \cdot \vec{b}$ is equal to :