ABC is a tringle and D ,E,F are the middle points of the sides . Forces represented by AD, 2/3 BE and 1/3 CF act on a particle at the point where AD and BE meet.Show that the resultant is represunted in magnitude and direction by 1/2 AC and that its line of action divided in the ratio 2:1.

Find a point O within a tringle ABC so that the forces represented by OA ,OB and OC in magnitude and direction and acting at O,may be in equalibrium.

If G is the centriod of tringle ABC, Show that : 

1) Forces acting on a particle and represented  by GA, GB, GC are in equalibrium .

2) Forces is represented by GD,GE, GF are in equalibrium , where D,E, F are mid points of BC,AC and AB repectively.

P is any point on tringle ABC and D,E,F are the mid point of the sides . prove that forces represented by AP, BP, CP, PD, PE, PF are in equalibium.

If P is the point in any plane of the tringle ABC  show that the forces PA, PB, PC are equal to 3PG, where G is the centriod of the tringle.

ABCD is a quadrilateral. Forces is represent by BC, BA, DC, DA are acting at a point . show that the resultant will be represented by four times the line joining the mid points of the diagonal.

ABCD is a Quadriletral and E is the point of intersection of the lie of joining the middle point of the oppsite sides . Prove that the resultant of the forces represented by OA ,OB, OC, OD, is given by 4OE wherever the point O may be . when will these forces be in equalibrium.

If P,Q,R,S be the middle point the side of a quadilatral ABCD and O is any point , show that the forces represented by OA, OB, OC, OD have same resultant as the forces represented  by OP, OQ, OR, OS.

ABCD is a parallelogram and P is any point in its plane . A particle P is attracted towards A and C by forces proportional to PA and PC respect. and repel from B and D by forces proportional to BP and DP respectvely. show that P is in equalibrium in all positions.

Show that the resultant of the forces OA tanA and OB tanB acting along the sides OA and OB of a tringle OAB is AB. tanB.tanA and act in the direction of the perpendicular from O on AB.

O is a point in the plane of tringle ABc. AO meets BC in D Show that component along AB and AC respectively of the forces represented by AD are 

1) 1/2 AB and 1/2 Ac if O is te centriod.

2) \(b\over(b+c) \) AB and \(c\over(b+c)\) AC if O is the incentre.

3) \(tanB\over(tanB+tanC)\)AB and \(tanC\over(tanB+tanC)\) AC if O is the orhogonal of the triangle.