In coordinate space, the equation of the plane that is perpendicular to the line $\frac { x - 2 } { 2 } = \frac { y - 2 } { 3 } = z - 1$ and passes through the point $( 1 , - 5,2 )$ is $2 x + a y + b z + c = 0$. Find the value of $a + b + c$. [3 points]