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Question: Answered & Verified by Expert
Let $A B C D E F$ be a regular hexagon with the vertices $A, B, C, D, E$ and $F$ counter clockwise. Then, the vector $\mathbf{A B}+\mathbf{B C}$ is equal parallel to
MathematicsVector AlgebraAP EAMCETAP EAMCET 2021 (23 Aug Shift 1)
Options:
  • A $B C+C D$
  • B $C D+D E$
  • C $A F+F E$
  • D $F E+E D$
Solution:
2667 Upvotes Verified Answer
The correct answer is: $F E+E D$



$$
\begin{aligned}
\mathbf{A B}+\mathbf{B C} & =\mathbf{A C} \\
\text { and } \mathbf{F E}+\mathbf{E D} & =\mathbf{F D}
\end{aligned}
$$

Since, $A B C D E F$ is regular hexagon.
AC must be parallel to FD.
$\therefore \mathbf{A B}+\mathbf{B C}$ is parallel to $\mathbf{F E}+\mathbf{E D}$.

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