Question

In a regular hexagon \( ABCDEF \), if \( \overrightarrow{AB} = \mathbf{a} \) and \( \overrightarrow{BC} = \mathbf{b} \), then find \( \overrightarrow{FA} \).

• A. \( \mathbf{a} - \mathbf{b} \)
• B. \( \mathbf{a} + \mathbf{b} \)
• C. \( \mathbf{b} - \mathbf{a} \)
• D. \( 2\mathbf{b} - \mathbf{a} \)

Hint:

For a regular hexagon, opposite vectors satisfy symmetry properties, simplifying calculations.

Answer 1

The Correct Option is A

Using vector properties of a regular hexagon: \[ \overrightarrow{FA} = \overrightarrow{AB} - \overrightarrow{BC} \] \[ = \mathbf{a} - \mathbf{b} \] Thus, the correct answer is \( \mathbf{a} - \mathbf{b} \).