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