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If a, b a...

Question

If $a$ , $b$ are the vectors forming consecutive sides of a regular hexagon $A B C D E F$ , find the correct option?

\to C E = 2 b - a

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\to C E = b - 2 a

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\to A E = 2 b - a

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\to A E = b - 2 a

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Solution

The correct option is C $\to C E = b - 2 a$
$\to A B = a, \to B C = b$
$∴ \to A C = \to A B + \to B C = a + b$ ...(1)
$\to A D = 2 \to B C = 2 b$ ...(2)
( $∵$ AD is parallel to BC and twice its length).
$\to C D = \to A D - \to A C = 2 b - (a + b) = b - a$ ...(3)
$\to F A = - \to C D = a - b$ ...(4)
$\to D E = - \to A B = - a$ ...(5)
$\to E F = - \to B C = - b$ ...(6)
$\to A E = \to A D + \to D E = 2 b - a$ by (2) and (5) ...(7)
$\to C E = \to C D + \to D E = b - a - a = b - 2 a,$ by (3) and (5) or
$\to C E = \to A E - \to A C = 2 b - a - (a + b) = b - 2 a$ by (1) and (7)

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