A person standing at the junction (crossing) of two straight paths represented by the equations $2x – 3y + 4 = 0$ and $3x + 4y – 5 = 0 $ wants to reach the path whose equation is $6x – 7y + 8 = 0$ in the least time. Find equation of the path that he should follow.

Question

$\begin {array} {1 1} (A)\;119x-102y=125 & \quad (B)\;-119x+102y=125 \\ (C)\;119x+102y=-125 & \quad (D)\;119x+102y=125 \end {array}$