# Forces of magnitude aF,bF,aF,bF and cF act respectively along the sides BA,BC,DC,DA and the diagonal BD of a rectangle ABCD, where a=AB, b=BC and c=BD, in the directions specified by the order of...

Forces of magnitude aF,bF,aF,bF and cF act respectively along the sides BA,BC,DC,DA and the diagonal BD of a rectangle ABCD, where a=AB, b=BC and c=BD, in the directions specified by the order of letters. Show that the system equivalent to a single force and find its magnitude, direction and line of action.

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Forces of magnitude aF,bF,aF,bF and cF act respectively along the sides BA,BC,DC,DA and the diagonal BD of a rectangle ABCD, where a=AB, b=BC and c=BD, in the directions specified by the order of letters. Show that the system equivalent to a single force and find its magnitude, direction and line of action.

Consider a triangle BAD.Forces acting along a direction taken in order,along BA is aF ,along AD -bF and along BD is cF. By triangle law, Resultant is

BD=BA+AD

cF=aF-bF (i)

Consider a triangle BCD.Forces acting along a direction taken in order,along BC is bF ,along CD -aF and along BD is cF. By triangle law, Resultant is

BD=BC+CD

cF=bF-aF (ii)

From

(i) and (ii)

2cF=0

cF=0

=> **resulatnt of the forces is zero.**