This law is used to add more than two vectors. The above figure
illustrates four vectors Each of
these vectors is displaced parallel to itself so that all four of them touch each other as
shown in the figure (b). Obviously vector
will be the resultant of
.
Thus, the law can be stated in the following way.
If a number of vectors can be represented both in magnitude and direction by the sides of an open convex polygon taken in the same order, then the resultant is represented completely in magnitude and direction by the closing side of the polygon, taken in the opposite order.
This law can easily be proved by applying
the law of triangle of vectors to the figure. From the DABC,
we have,
From the DACD,
From the DADE,
The resultant
Corollary
If a number of vectors are represented by the sides of a closed polygon taken in order, then, their resultant is zero.
Another important definition to remember is that of the equilibrant vector. An equilibrant vector is a single vector which balances two or more vectors acting simultaneously at a point. The equilibrant and the resultant vectors are equal in magnitude and opposite in direction.
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Each of
these vectors is displaced parallel to itself so that all four of them touch each other as
shown in the figure (b). Obviously vector
will be the resultant of
.
Thus, the law can be stated in the following way.
