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 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 the plane passing through (1,2,0) which contains the line (x+3)/3=(y-1)/4=(z-2)/(-2)

Find the equation of the lines through the point (3, 2) which make an angle of 45 with the line x-2y=3 .

Find the equation of the lines through the point (3, 2) which make an angle of 45^@ with the line x-2y=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

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

Find the equation of the line drawn through point (1, 0, 2) to meet the line (x+1)/3=(y-2)/(-2)=(z1)/(-1) at right angles.

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

Find the equation of the sphere which has centre at the origin and touches the line 2(x+1)=2-y=z+3.

Find the equation of the line joining the origin to the point of intersection of 4x+3y=8 and x+y=1 .