good morning friends explain polygon law of addition (for vectors)
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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.
Hope this helps u dude. I have also proved this law. So that it will be easy
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.
Hope this helps u dude. I have also proved this law. So that it will be easy
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