Let A1 A2 A3 A4 A5 A6 A1 be a regular hexagon. Write the x- components of the vectors represented by the six sides taken in order. Use the fact that the resultant of these six vectors is zero, to prove that
cos0+cosπ/3+cos2π/3+cos3π/3+cos4π/3+cos5π/3=0
Use the known cosine values to verify the result.
BrainlyYoda:
Concept of Physics - 1 , HC VERMA , Chapter - "Physics and Mathematics"
Answers
Answered by
76
Thanks for asking the question!
ANSWER::
The thing which we knows is that according to polygon vector addition , the resultant of these vectors is 0.
In magnitude terms , A=B=C=D=E=F
So, resultant of x component=Acos0+Acosπ/3+Acos2π/3+Acos3π/3+Acos4π/3+Acos5π/3 = 0
As resultant is 0 , x component of resultant = 0
i.e. cos0+cosπ/3+cos2π/3+cos3π/3+cos4π/3+cos5π/3 = 0
And same as we proved above,
sin0+sinπ/3+sin2π/3+sin3π/3+sin4π/3+sin5π/3 = 0
Hope it helps you!
ANSWER::
The thing which we knows is that according to polygon vector addition , the resultant of these vectors is 0.
In magnitude terms , A=B=C=D=E=F
So, resultant of x component=Acos0+Acosπ/3+Acos2π/3+Acos3π/3+Acos4π/3+Acos5π/3 = 0
As resultant is 0 , x component of resultant = 0
i.e. cos0+cosπ/3+cos2π/3+cos3π/3+cos4π/3+cos5π/3 = 0
And same as we proved above,
sin0+sinπ/3+sin2π/3+sin3π/3+sin4π/3+sin5π/3 = 0
Hope it helps you!
Attachments:
Answered by
2
Explanation:
ANSWER
According to polygon vector addition, the resultant of given vectors is zero.
In the term of magnitude, A
1
=A
2
=A
3
=A
4
=A
5
=A
6
=A
So, resultant of X component=
=Acos0+Acos
3
Π
+Acos
3
2Π
+Acos
3
3Π
+Acos
3
4Π
+Acos
3
5Π
=0
As resultant zero, X component= 0 and same is proved in the given data
Similar questions