If the adjacent sides of a rectangle are $\bar{a}=5 \bar{m}-3 \bar{n}, \bar{b}=-\bar{m}-2 \bar{n}$ and the adjacent sides of another rectangle are $\bar{c}=-4 \bar{m}-\bar{n}, \bar{d}=-\bar{m}+\bar{n}$, then the angle between the vectors $\bar{x}=\frac{\bar{a}+\bar{c}+\bar{d}}{3}$ and $\bar{y}=\frac{\bar{c}+\bar{d}}{5}$ is

• A

  $\frac{\pi}{2}$
• Correct answer
  B

  $\operatorname{Cos}^{-1}\left(\frac{19}{5 \sqrt{43}}\right)$
• C

  $\operatorname{Cos}^{-1}\left(\frac{19}{5 \sqrt{43}}\right)+\pi$
• D

  $\operatorname{Sin}^{-1} \frac{19}{4 \sqrt{43}}$

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