Find the equation of the plane containing the lines 2x-y+z-3=0,3x+y+z=5 and a t a distance of `1/sqrt6` from the point (2,1,-1).

Let the equation of the plane containing the line x-y - z -4=0=x+y+ 2z-4 and is parallel to the line of intersection of the planes 2x + 3y +z=1 and x + 3y + 2z = 2 be x + Ay + Bz + C=0 Compute the value of |A+B+C| .

Find the equation of the image of the plane x-2y+2z-3=0 in plane x+y+z-1=0.

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 the plane passing thruogh the line of intersection of the planes x +2y + 3z = 2 and x - y + z= 3 , and at a distance (2)/(sqrt(3)) from point (3,1,-1).

Find the equation of the plane containing the line (y)/(b)+(z)/(c)=1,x=0 , and parallel to the line (x)/(a)-(z)/(c)1,y=0 .

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

Find the equation of a plane which is parallel to the plane x-2y+2z=5 and whose distance from thepoint (1,2,3) is 1.

Find the equation of the plane containing the lines (x-5)/4=(y-7)/4=(z+3)/(-5)a n d(x-8)/7=(y-4)/1=(z-5)/3dot

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 plane containing the line of intersection of the planes x + y + z - 6 = 0 and 2x + 3y + 4z + 5 = 0 and passing through the point (1,1,1)