Show that the two lines `x+1/3=y+3/5=z+5/7` and `x-2/1=y-4/3=z-6/5` intersect each other. Find also the point of intersection.

Show that the two lines (x-1)/2=(y-2)/3=(z-3)/4 and (x-4)/5=(y-1)/2=z intersect each other . Find also the point of intersection.

Show that the lines : (x+1)/3=(y+3)/5=(z+5)/7 and (x-2)/1=(y-4)/3=(z-6)/5 intersect each other. Also find their point of intersection.

Show that the two lines (x-5)/4=(y-7)/4=(z+3)/-5 and (x-8)/7=(y-4)/1=(z-5)/3 intersect each other . Find also the point of intersection.

The lines x+3y-1=0 and x-4y=0 intersect each other. Find their point of intersection.

Show that the lines (x+1)/-3=(y-3)/2=(z+2)/1 and x/1=(y-7)/-3=(z+7)/2 intersect. Find the point of intersection and the equaion of the plane contianing them.

Show that the lines: (x-1)/3=(y+1)/2=(z-1)/5 and (x-2)/4=(y-1)/3=(z+1)/-2 do not intersect.

Show that the lines (x-1)/23=(y+1)/2=(z-1)/5 and (x-2)/4=(y-1)/3=(z+1)/-2 do not intersect.

Show that the lines (x-5)/7 = (y+2)/-5 = z/1 and x/1 = y/2 = z/3 are perpendicular to each other

A line with direction numbers is drawn to intersect the lines (x-5)/3=(y-7)/-1=(z+2)/1 and (x+3)/-3=(y-3)/2=(z-6)/4 . find the coordinates of the points of intersection of the length intercept on it.