Question:
In a regular hexagon \( ABCDEF \), if \( \overrightarrow{AB} = \mathbf{a} \) and \( \overrightarrow{BC} = \mathbf{b} \), then find \( \overrightarrow{FA} \).
In a regular hexagon \( ABCDEF \), if \( \overrightarrow{AB} = \mathbf{a} \) and \( \overrightarrow{BC} = \mathbf{b} \), then find \( \overrightarrow{FA} \).
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For a regular hexagon, opposite vectors satisfy symmetry properties, simplifying calculations.
Updated On: Mar 19, 2025
- \( \mathbf{a} - \mathbf{b} \)
- \( \mathbf{a} + \mathbf{b} \)
- \( \mathbf{b} - \mathbf{a} \)
- \( 2\mathbf{b} - \mathbf{a} \)
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The Correct Option is A
Solution and Explanation
Using vector properties of a regular hexagon:
\[
\overrightarrow{FA} = \overrightarrow{AB} - \overrightarrow{BC}
\]
\[
= \mathbf{a} - \mathbf{b}
\]
Thus, the correct answer is \( \mathbf{a} - \mathbf{b} \).
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