Consider two planes $P_1:2x-3y+z=-5$  and  .$P_2:x-4y-14z=5$.  If a line L which is perpendicular to line of intersection of planes $P_{1}and{P}_2$  whose  one point $A\left(-7,\text{\hspace{0.33em}}{y}_1,z_1\right)$ lies on the plane $P_1$  and point $B\left(x_2,\text{\hspace{0.33em}}{y}_2,z_2\right)$  and $C\left(x_3,\text{\hspace{0.33em}}{y}_3,z_3\right)$  lie on plane $P_2$ has the equation $\frac{x+7}{a}=\frac{y-y_1}{-b}=\frac{z-z_1}{c}$ , where $a,\text{\hspace{0.33em}}b,c\in N$ , then: