Find the equation of the line passing through the point (-1, 3, -2) and perpendicular to the lines x=y/2=z/3 and x+2=y/4=z+15

Let the direction ratios of the required line be a, b, c. Since the required line is perpendicular to the given lines, therefore,a+2b+3c=0—(1)a+4b+5c=0—(2)Solving (1) and (2), by cross multiplication, we geta/10=b/(-8)=c/2+6=k⇒a=4k,b=-8k,c=8kThus, the required line passing through P(-1, 3, -2) andhaving the direction ratios a=4k,b=-8k,c=8kisx+1/4=y-3/-8=z+2/8orx+1/2=y-3/-4=z+2/4which is the required equation of the line.