Find the equation of the plane perpendicular to the line `(x-1)/2=(y-3)/(-1)=(z-4)/2` and passing through the origin.

Find the vector and cartesian equations of the plane containing the line (x-2)/(2)=(y-2)/(3)=(z-1)/(-2) and passing through the point (-1, 1,-1).

Find the equation of a line perpendicular to the line x - 2y + 3 = 0 and passing through the point (1, -2) .

Find the equation of the line perpendicular to the line x/a-y/b=1 and passing through a point at which it cuts the x-axis.

Find the equation of the plane passing through the line (x-1)/5=(y+2)/6=(z-3)/4 and point (4,3,7)dot

Find the equation of the projection of the line (x-1)/2=(y+1)/(-1)=(z-3)/4 on the plane x+2y+z=9.

Find the equation of the plane passing through the straight line (x-1)/2=(y+2)/(-3)=z/5 and perpendicular to the plane x-y+z+2=0.

Find the equation of a line through (-1,3) perpendicular to the line 2x + 3y + 1 = 0.

Find the equation of the line passing through the intersection (-1,2,3) and perpendicular to the lines (x-1)/2=(y-2)/(-3)=(z-3)/4a n d(x-4)/5=(y-1)/2=zdot and also through the point (2,1,-2)dot

Find the Vector and Cartesian equation of the plane containing the line (x-2)/2=(y-2)/3=(z-1)/3 and parallel to the line (x+1)/3=(y-1)/2=(z+1)/1