For two given vectors $\bar{a}$ and $\bar{b}$ if the vectors $\overline{\mathrm{A}}, \overline{\mathrm{B}}$ are such that $\overline{\mathrm{A}}+\overline{\mathrm{B}}=\bar{a}, \overline{\mathrm{A}} \times \overline{\mathrm{B}}=\bar{b}$ and $\overline{\mathrm{A}} \cdot \bar{a}=1$, then $\overline{\mathrm{A}}=$

• Correct answer
  A

  $\frac{(\bar{a} \times \bar{b})+\bar{a}}{\bar{a}^2}$
• B

  $\frac{(\bar{b} \times \bar{a})+\bar{a}\left(\bar{a}^2-1\right)}{\bar{a}^2}$
• C

  $\frac{\bar{a}\left(\bar{a}^2-1\right)+\bar{b}\left(\bar{b}^2-1\right)}{\bar{a}^2+\bar{b}^2}$
• D

  $\frac{(\bar{a} \times \bar{b})+\bar{b}}{\bar{b}^2}$

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