Question

state and prove polygon law of vector addition

Answer 1

Polygon Law of Vector Addition:
If two or more vectors are represented by adjacent sides of a polygon taken in same order in both direction and magnitude ,then the resultant is given by closing the side of polygon in opposite direction.

Proof:
Let there be a polygon of n-sides (Here 5 -sides) .
In Triangle ABC,
By triangle law of vector addition,
AB + BC = AC ( All are in vector form) ---(1)
And,
Similarly,
AC + CD = AD ---(2)
&
AD + DE = AE ----(3)

Similarly, we will do this for all sides in polygon ( Here 5-sides) .

Them, Add all these equations. we get,
AB + BC +CD + DE = AE.
AE = Closing side (Resultant) , other are normal vector sides .

For n-sides, it can be written analogously and stated as above theorem.

Answer 2

Answer:

Polygon Law of Vector Addition:

If two or more vectors are represented by adjacent sides of a polygon taken in same order in both direction and magnitude ,then the resultant is given by closing the side of polygon in opposite direction.

Proof:

Let there be a polygon of n-sides (Here 5 -sides) .

In Triangle ABC,

By triangle law of vector addition,

AB + BC = AC ( All are in vector form) ---(1)

And,

Similarly,

AC + CD = AD ---(2)

&

AD + DE = AE ----(3)

Similarly, we will do this for all sides in polygon ( Here 5-sides) .

Them, Add all these equations. we get,

AB + BC +CD + DE = AE.

AE = Closing side (Resultant) , other are normal vector sides .