Let $\overrightarrow{a}$ and $\overrightarrow{b}$ be two non-zero vectors perpendicular to each other and $\left|\overrightarrow{a}\right|=\left|\overrightarrow{b}\right|$, If $|\overrightarrow{a}\times \overrightarrow{b}|=\left|\overrightarrow{a}\right|$, then the angle between the vectors
$(\overrightarrow{a}+\overrightarrow{b}+(\overrightarrow{a}\times \overrightarrow{b}\left)\right)$ and $\overrightarrow{a}$ is equal to :

• A

  ${\sin }^{-1}\left(\frac{1}{\sqrt{3}}\right)$
• Correct answer
  B

  ${\cos }^{-1}\left(\frac{1}{\sqrt{3}}\right)$
• C

  ${\cos }^{-1}\left(\frac{1}{\sqrt{2}}\right)$
• D

  ${\sin }^{-1}\left(\frac{1}{\sqrt{6}}\right)$

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