Explain the parallelogram law, please.

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gsenviro | College Teacher | (Level 1) Educator Emeritus

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I assume that you are referring to Parallelogram Law of force which makes use of similar identity we use for vectors addition. It is used to determine the resultant force and its direction when two forces are applied to an object.

If two force F1 and F2, applied to an object, are oriented at an angle '`theta` ' with each other, we can connect the two forces at their tails and draw lines from their tips (or heads) and complete a parallelogram. The resultant force, Fr will act along the diagonal (emanating from the tails of these two forces) of this parallelogram.

This resultant force will be the vector sum of two forces and is given by cosine law as:

`Fr = sqrt(F1^2 + F2^2 +2F1F2cos theta)`

and the direction of this resultant will be given in terms of the angle it makes with the base of parallelogram (F1) and is given asĀ 

`alpha = tan^(-1) [(F2sin theta)/(F1+F2 cos theta)]`

Hope this helps.

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