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.

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