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(A) Let the vertices of the regular hexagon be $O, A, B, C, D, E$ in order. Let $\vec{OA} = a$ and $\vec{AB} = b$. In a regular hexagon,the sides are

Vedclass · Accepted Answer

$a-b, -a, -b, b-a$

Vedclass · Answer

(A) Let the vertices of the regular hexagon be $O, A, B, C, D, E$ in order. Let $\vec{OA} = a$ and $\vec{AB} = b$. In a regular hexagon,the sides are equal in magnitude and parallel to opposite sides. The vectors representing the sides in order are: $1$. $\vec{OA} = a$ $2$. $\vec{AB} = b$ $3$. $\vec{BC} = \vec{OA} - \vec{AB} = a - b$ $4$. $\vec{CD} = -\vec{OA} = -a$ $5$. $\vec{DE} = -\vec{AB} = -b$ $6$. $\vec{EO} = -\vec{BC} = -(a - b) = b - a$ Thus,the remaining four sides are $a - b, -a, -b, b - a$.

If vectors $a$ and $b$ represent two consecutive sides of a regular hexagon,then the vectors representing the remaining four sides in order are:

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