State Polygon law of vector addition and prove it using Triangle law of vector addition.

Explanation

Statement: If a number of vectors are represented both in magnitude and direction by the sides of a polygon taken in the same order, then the resultant vector is represented both in magnitude and direction by the closing side of polygon taken in opposite order.
Proof: Consider four vectors `vec A , vec B, vec C and vec D` as shown in the figure.`vec R` represents the resultant of the vectors. Join OQ and OR. Applying triangle law of vector addition to `DeltaOPQ .`
`vec (OQ) = vec (OP) +vec ( PQ)`
`or vec (OQ) = vec A + vec B " "...(i)`
From `Delta OQR vec (OR) + vec (OQ) + vec (QR)`
`vec (OR) = vec A + vec B + vec C" "...(ii)`
Applying triangle law of vector addition to `Delta ORS,` we get
`vec ( OS) = vec (OR) + vec ( RS) or vec R = vec A+ vec B + vec C + vec D`
This proves the polygon law of vector addition.