If a and b makes an angle cos^-1(5/9) with each other, then | a + b |=√ 2 | a - b | for | a |=n| b | The integer value of n is ____.

If $\displaystyle \vec{a}$ and $\displaystyle \vec{b}$ makes an angle $\displaystyle \cos ^{-1}\left(\frac{5}{9}\right)$ with each other, then $\displaystyle |\vec{a}+\vec{b}|=\sqrt{2}|\vec{a}-\vec{b}|$ for $\displaystyle |\vec{a}|=n|\vec{b}|$ The integer value of n is $\displaystyle \_\_\_\_$.