Find the equations of the line passing through the point(1,-2,3) and parallel to the line (x-6)/3=(y-2)/(-4)=(z+7)/5

(x-6)/3=(y-2)/(-4)=(z+7)/5     

hence, the direction ratios of the line are (3,-4,5)

Since for a parallel line, the direction ratios remain the same, hence equation of line parallel to the given line and passing through (1,-2,3) is given by 

 

(x-1)/3 = (y+2)/(-4) = (z-3)/5