Kinematics: JEE Main 2023 Physics question

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