Let $a=\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}},b=2\hat{\mathrm{i}}+2\hat{\mathrm{j}}+\hat{\mathrm{k}}$ and $c=5\hat{\mathrm{i}}+\hat{\mathrm{j}}-\hat{\mathrm{k}}$ be three vectors. The area of the region formed by the set of points whose position vectors $\overrightarrow{r}$ satisfy the equations $r·a=5$  and $|r-b|+|r-c|=4$ is closest to the integer.

• Correct answer
  A

  $4$
• B

  $9$
• C

  $14$
• D

  $19$

Hence, the correct answer is option: 'A'.