True or False :
The line 2x + y =3 divides the join of (0,0) and (2,2) in the ratio 1:1.

Prove that the st. line ax + by + c = 0 divides the join of (x_1, y_1) and (x_2, y_2) in the ratio -(ax_1 + by_1 +c)/(ax_2+ by_2+c) .

Find the co-ordinates of the point R, which divides the join of P (0, 0, 0) and Q (4, -1, -2) in the ratio 1 : 2 externally and verify that P is the mid-point of [RQ].

True or false The line x=y=z lies in the plane x-2y+z-1=0.

The plane XOZ divides the join of (1, -1, 5) and (2, 3, 4) in the ratio of lambda:1 , then lambda is

Let (x,y) be any point on the parabola y^2= 4x . Let P be the point that divides the line segment from (0, 0) to (x, y) in the ratio 1 : 3. Then the locus of P is:

A line perpendicular to the line segment joining the points (1,0) and (2,3) divides it in the ratio 1 : n. Find the equation of the line.

Ratio in which the zx-plane divides the join of (1, 2, 3) and (4, 2, 1) .

If the line 2x+y=k passes through the point which divides the line segment joining the points (1,1) and (2,4) in the ratio 3:2 then k-equals.

Find the coordinates of a point which divides externally the line joining (1, -3) and (-3, 9) in the ratio 1 : 3.