D,E divide sides BC and CA of a triangle ABC in the ratio 2:3 respectively. Find the position vector of the point of intersection of AD and BE and the ratio in which this point divides AD and BE.

In triangleABC, D divides BC in the ratio l:m, G divides AD in the ratio (l+m):n then the position vector of G is

In ABC,D and E are the mid-points of AB and AC respectively.Find the ratio of the areas of ADE and ABC.

The points D,E,F divide BC,CA and AB of the triangle ABC in the ratio 1:4,3:2 and 3:7 respectively and the point divides AB in the ratio 1:3, then (AD+bar(BE)+bar(CF)):CK is equal to

In Delta ABC, D and E are the midpoint of AB and AC respectively. Find the ratio of the areas of Delta ADE and Delta ABC .

In a triangle ABC,D and E are points on BC and AC, respectivley,such that BD=2DC and AE=3EC. Let P be the point of intersection of AD and BE. Find BP/PE using the vector method.

If position vectors of the points A, B and C are a, b and c respectively and the points D and E divides line segment AC and AB in the ratio 2:1 and 1:3, respectively. Then, the points of intersection of BD and EC divides EC in the ratio

If position vectors of the points A, B and C are a, b and c respectively and the points D and E divides line segment AC and AB in the ratio 2:1 and 1:3, respectively. Then, the points of intersection of BD and EC divides EC in the ratio

If position vectors of the points A, B and C are a, b and c respectively and the points D and E divides line segment AC and AB in the ratio 2:1 and 1:3, respectively. Then, the points of intersection of BD and EC divides EC in the ratio