Show that the plane `ax+by+cz+d=0` divides the line joining `(x_1, y_1, z_1) and (x_2, y_2, z_2)` in the ratio of `(-(ax_1+ay_1+cz_1+d)/(ax_2+by_2+cz_2+d))`

The ratio in which the plane 4x+5y-3z=8 divides the line joining the points (-2,1,5) and (3,3,2) is

The point (4,2) divides the line segment joining (5,-1) and (2,y) in the ratio 1:2 .Find y .

Find the coordinates of the mid-point of the line joining the points (x_1, y_1) and (x_2, y_2).

Derive the formula to find the co-ordinates of a point which divide the line joining the points A(x_1,y_1,z_1) and B(x_2,y_2,z_2) internally in the ratio m:n .

Derive an expression for the co-ordinates of points that divides the linejoining points A(x_1,y_1,z_1) andB(x_2,y_2,z_2) internally in the ratio m:n.Hence find the co-ordinates of midpoint of AB where A=(3,2,1) and B=(7,6,5).