Polygon law of vectors is useful in adding more than two vectors, graphically. Let A, B, C, D and E be the vectors to be added.
R = A + B + C + D + E
Draw a polygon with consecutive sides taken in cyclic order, representing in magnitude and direction the vectors to be added. The resultant R, is represented by the closing side of the polygon taken in opposite order. This is shown in Fig.
When vectors to be added form a closed polygon; the resultant is zero.
Note the important properties of vector addition.
(1) Vector addition is commutative, i.e.
A + B = B + A
(2) Vector addition is associative, i.e.
A + (B + C) = B + (C + A) = C + (A +B)
(3) Vector addition in distributive, i.e.
m(A + B) = mA + mB
