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

• A
  $\frac{1}{2}$
• B
  $-1$
• ✓
  $-\frac{1}{2}$
• D
  $-\frac{3}{2}$