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Discussion Response Post to: Vectors

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Soumen Goswami (2446)

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total posts: 1777
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You can geometrically find the anticlockwise angles the sides of the hexagon make with the +X axis. They are 0,

/3, 2

/3,

( = 3

/3), 4

/3, 5

/3
Suppose the length of the hexagon side be L.
Then the X components are
L = L cos0
L cos

/3
L cos2

/3
-L = L cos

= L cos3

/3
L cos4

/3
Lcos5

/3
The vectors A₁, A₂, ...A₆ form a closed hexagon and hence their resultant is zero.
Then the X component of their resultant must also be zero. The X component of the resultant is the sum of the X components of the individual vectors. Hence
L cos0 + L cos

/3 + L cos2

/3 + L cos3

/3 + L cos4

/3 + Lcos5

/3 = 0
cos0 + cos

/3 + cos2

/3 + cos3

/3 + cos4

/3 + cos5

/3 = 0

All men dream but not equally. Those who dream by night in the dusty recesses of their minds wake in the day to find that it was vanity; but the dreamers of the day are dangerous men, for they may act their dream with open eyes to make it possible.

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