Accelerating Along a Plane

In the $xyz$ coordinate system, a massive particle is confined to the plane described by the equation below:

$x + 2y +3 z = 0$

The particle can slide along the plane without any resistance to its motion (such as friction). There is an ambient gravitational field such that a free particle would experience an acceleration in the $z$ -direction with a value of $-g$ .

If the magnitude of the confined particle's acceleration is equal to $\alpha g$ , what is the value of $\alpha$ (to 3 decimal places)?