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leehufford
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Homework Statement
We are supposed to compute the magnitude of vectors that make up a regular hexagon. We are given the magnitude of one side (its magnitude is 1).
We are also supposed to compute one of the interior angles.
Homework Equations
I feel like this isn't enough information to put into any equation I know.
The Attempt at a Solution
Obviously because it's a regular hexagon, all sides (vectors in the plane) are of equal length to each other.
Also, I am aware of this fact: each time a side is added to a polygon, 180 degrees is added to the total of the interior angles. A triangle is 180 degrees, square is 360, pentagon is 540 and hexagons are 720, which would make each interior angle 120 degrees.
But I believe the professor wants us to use linear algebra to show this, especially since the directive compute was given. I think my attempt at a solution is just deductive reasoning/ inference. Does anyone know of a way to use linear algebra to find these values? The hexagon has a vertex at the origin and one vector is aligned with the x axis, which means part of the hexagon is in the second quadrant. Any help would be greatly appreciated. Thanks in advance,
Lee
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