$\bar{a}, \bar{b}$ are position vectors of the points $A$ and $B$ respectively, $C$ and $D$ are points on the line AB such that $\overline{\mathrm{AB}}, \overline{\mathrm{AC}}$ and $\overline{\mathrm{BD}}, \overline{\mathrm{BA}}$ are two pairs of like vectors. If $\overline{\mathrm{AC}}=3 \overline{\mathrm{AB}}$ and $\overline{\mathrm{BD}}=2 \overline{\mathrm{BA}}$, then $\overline{\mathrm{CD}}=$

• A

  $3 \overline{\mathrm{~b}}-4 \overline{\mathrm{a}}$
• Correct answer
  B

  $4 \overline{\mathrm{a}}-4 \overline{\mathrm{~b}}$
• C

  $4 \bar{a}-3 \bar{b}$
• D

  $3 \bar{b}-3 \bar{a}$

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