If the forces of magnitude  P,Q,R act at a poitparallel to the sides BC, CA, AB respectively of a tringle ABC, Prove that the magnitude of the resultant is 

\( \sqrt{P^2+Q^2+R^2-QRcosA-2RPcosB-2PQcosC}\)

The force acting at a point are parallel to the sides of tringle ABC taken in order and are proportional to the cosine of the opposite angle. show that their resultant is proportional to

 \(\sqrt{1-cosAcosBcosC}\).

Five forces acting at a point O are in equallibrium, four of them whose magnitude 3,4,4,3 kg wt. act along the coplanar line OA, OB, OC,ODrespectively, such that 

\(\angle{AOB=45^{\circ}},\angle{BOC=60^\circ},\angle{COD=15^\circ}\).

ABCD is a quadilateral with AB=2cms,BC=3cms, DA=7cms. Forces of 6,9,15,20 gms.wt.act on a particle parallel to the respective side of the quadilataral . Show that their resultant is a force of 1gmwt. parallel to AD.

Forces of 6,8,12 kg. wt. act along BC,CA, AB of the sides of tringle of lengths 3,4,5 cm respectively .Show that their resultant of forces of 2kg wt. acting parallel to AB.

ABCDEF is a regular hexagon. force of magnitude \(1, 2\sqrt3,2,4\sqrt3,5N\) respectively act at one of the angular points of the hexagon towards the five others in order. Find the magnitue and the direction of the resultant forces.

ABCDEF is a regular hexagon.Find the direction and magnitude of resultant of forces equal to7,18,5,9 and 19kg. wt. acting along A respectively along AB,CA,AD,AE,AF,

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