Show that the plane ax + by + cz + d = 0 divides, the line segment joining the points `(x_1, y_1, z_1)` and `(x_2, y_2, z_2)` in the- ratio `-(ax_1+by_1+cz_1+d)/(ax_2+by_2+cz_2+d)`.

Show that the plane ax+by+ca+d=0 divides the line joining the points (x_1,y_1,z_1) & (x_2,y_2,z_2) in the ratio - (ax_1+by_1+cz_1+d_1)/(ax_2+by_2+cz_2+d_2)

Find the ratio in which the plane 2x+3y+5z=1 divides the line segment joining the points (1,0,-3)and (1,-5,7).

The line segment joining the points (1,2) and (-2, 1) is divided by the line 3x+4y=7 in the ratio

Find the ratio in which the plane 2x + 2y - 2z = 1 divides the line segment joining the points A(2,1, 5) and B(3, 4, 3). Find the co¬ ordinate of point of contact.

A straight line joining the points (1, 1, 1) and (0, 0, 0) intersects the plane 2x+2y+z=10 at

A straight line joining the point (1, 1, 1) and (0, 0, 0) intersects the plane 2x + 2y + z = 10 at-

the line joining the points (1,1,2) and (3,-2,1) meets the plane 3x+2y+z=6 is __

The ratio in which the line segment joining the points ( 1 , - 2 , 3) and ( 4 , 2 , - 1) is divided by the XOY plane is _

The line joining the points (1,1,2) and (3,-2,1)meets the plane 3x + 2y + z = 6 is

The points P divides the line - segment joining the points A(x_(1),y_(1))andB(x_(2),y_(2)) in the ratio m : n . If P lies on the line ax+by +c=0 , prove that, (m)/(n)=-(ax_(1)+by_(1)+c)/(ax_(2)+by_(2)+c) .