If the angle between the line $x=\frac{y-1}{2}=\frac{z-3}{\mathrm{\lambda }}$ and the plane $x+2y+3z=4$ is ${\cos }^{-1}\left(\sqrt{\frac{5}{14}}\right)$, then $\lambda$ equals 

Statement $\mathbf{1}$: The point $A\left(1,0,7\right)$ is the mirror image of the point $B\left(1,6,3\right)$ in the line $\frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3}$.

Statement $\mathbf{2}$: The line $\frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3}$ bisects the line segment joining $A\left(1,0,7\right)$ and $B\left(1,6,3\right)$.