Vector Algebra

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 ____________.