Find the vector and cartesian equations of the line which is perpendicular to the lines with equations$\frac{x+2}{1}=\frac{y-3}{2}=\frac{z+1}{4}\text{ and }\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}$and passes through the point $(1,1,1)$. Also find the angle between the given lines.