In a regular hexagon A BC D EF , A E =, A C + A F + A B, A C + A F − A B, A C + A B − A F, None of these

Obviously, A E = A C + C D + D E = A C + A F − A B , { C D = A F and D E = − A B }

In a regular hexagon A BC D EF , A E =

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In a regular hexagon $A B C D E F, \overrightarrow{A E}=$

MathematicsVector AlgebraJEE Main

Options:

A $\overrightarrow{A C}+\overrightarrow{A F}+\overrightarrow{A B}$
B $\overrightarrow{A C}+\overrightarrow{A F}-\overrightarrow{A B}$
C $\overrightarrow{A C}+\overrightarrow{A B}-\overrightarrow{A F}$
D None of these

Solution:

1785 Upvotes Verified Answer

The correct answer is: $\overrightarrow{A C}+\overrightarrow{A F}-\overrightarrow{A B}$

Obviously, $\overrightarrow{A E}=\overrightarrow{A C}+\overrightarrow{C D}+\overrightarrow{D E}$

$=\overrightarrow{A C}+\overrightarrow{A F}-\overrightarrow{A B},\{\overrightarrow{C D}=\overrightarrow{A F}$ and $\overrightarrow{D E}=-\overrightarrow{A B}\}$

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