Find the Cartesian equations of a line which passes through the point(1,2,3) and is parallel to the line (-x-2)/1=(y+3)/7=(2z-6)/3

(-x-2)/1=(y+3)/7=(2z-6)/3 

(x+2)/(-1) = (y+3)/7 = (z-3)/(3/2)

 

Hence, the direction ratios of the line are (-1, 7, 3/2). 

 

For parallel lines, the direction ratios remain the same, hence, the equation of line parallel to the given line but passing through (1,2,3) will be given by 

 

(x-1)/(-1) = (y-2)/7 = (z-3)/3/2

(-x+1)/1 = (y-2)/7 = (2z-6)/3