Find the equations of the two lines through the origin which intersect the line `(x-3)/2=(y-3)/1=z/1` at angle of `pi/3` each.

Find the equation of the two lines through the origin which intersects the line (x-3)/(2)=(y-3)/(1)=(z)/(1) at angles of (pi)/(3) each.

Find the equation of line through the origin and a point where line (x-1)/2=(y-2)/4=(z-3)/4 . Cuts the z-axis.

Find the equation of line through the origin and a point where line (x-1)/2=(y-2)/4=(z-3)/4 . Cuts the z-axis.

Joint equation of two lines through the origin, each making angle of 45^(@) with line 3x-y=0 is

Find the equation of the line passing through the point (3,1,2) and perpendicular to the lines (x-1)/1=(y-2)/2=(z-3)/3 and x/(-3)=y/2=z/5

Find the equations of the straight line passing through the point (1,2,3) to intersect the straight line x+1=2(y-2)=z+4 and parallel to the plane x+5y+4z=0.

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