Vectors a i +b j + k and 2 i -3 j +4 k are perpendicular to each other when 3 a+2 b=7, the ratio of a to b is x/2 The value of x is ____.

Vectors $\displaystyle a \hat{i}+b \hat{j}+\hat{k}$ and $\displaystyle 2 \hat{i}-3 \hat{j}+4 \hat{k}$ are perpendicular to each other when $\displaystyle 3 a+2 b=7$, the ratio of $\displaystyle a$ to $\displaystyle b$ is $\displaystyle \frac{x}{2}$ The value of $\displaystyle x$ is $\displaystyle \_\_\_\_$.