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.

A weight of 100kg  is supported by two ropes which are tied to the wt. and are inclined at angle 45 degree 30 degree to the verticle.Find the tension in the string.