[" Example "10." Find the equations of the line twhich intersects the lines "],[qquad (x-1)/(2)=(y-2)/(3)=(z-3)/(4)" and "(x+2)/(1)=(y-3)/(2)=(z+1)/(4)" and passes through the point "(1,1,1)" ."]

Find the point of intersection of the lines (x-1)/(2)=(y-2)/(3)=(z-3)/(4) and (x-4)/(5)=(y-1)/(2)=z .

" The point of intersection of lines "(x-1)/(2)=(y-2)/(3)=(z-3)/(4)" and "(x-4)/(5)=(y-1)/(2)=(z)/(1)" is "

(i) Find the equations of the straight line passing through the point (2,3,-1) and is perpendicular to the lines : ( x-2)/(2) = (y + 1)/(1) = (z - 3)/(-3) and (x - 3)/(1) = (y + 2)/(1) = (z - 1)/(1) . (ii) Find the equation of the line which intersects the lines : (x + 2)/(1) = (y - 3)/(2) = (z + 1)/(4) and (x - 1)/(2) = (y - 2)/(3) = (z - 3)/(4) Perpendicular and passes through the point (1,1,1) .

The point of intersection of lines (x-1)/(2)=(y-2)/(3)=(z-3)/(4) and (x-4)/(5)=(y-1)/(2)=(z)/(1) is

Find the equation of the line passing through the intersection of (x-1)/(2)=(y-2)/(-3)=(z-3)/(4) and (x-4)/(5)=(y-1)/(2)=z and also through the point (2,1,-2)

Find the equation of a line which passes through the point (1,1,1) and intersects the lines (x-1)/(2)=(y-2)/(3)=(z-3)/(4)and(x+2)/(1)=(y-3)/(2)=(z+1)/(4)

Find the equation of the line intersecting the lines (x-a)/(1)=(y)/(1)=(z-a)/(1) and (x+a)/(1)=(y)/(1)=(z+a)/(2) and parallel to the line (x-a)/(2)=(y-a)/(1)=(z-2a)/(3)

Find the equation of a line which passes through the point (1,1,1) and intersects the lines (x-1)/2=(y-2)/3=(z-3)/4a n d(x+2)/1=(y-3)/2=(z+1)/4dot