ABCDEF be a regular hexagon in the xy plane and $\vec{AB} = 4 i$ .Then $CD =$

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$6 i + 2 \sqrt{3} j$

$2 (- i + \sqrt{3} j)$

$2 (i + \sqrt{3} j)$

$2 (i - \sqrt{3} j)$

answer is B.

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Detailed Solution

$\sin 60^{\circ} = \frac{y}{4} \Rightarrow y = 2 \sqrt{3} \cos 60^{\circ} = \frac{x - 4}{4} x = 6 OC = 6 i + 2 \sqrt{3} j OD = 4 i + 4 \sqrt{3} j CD = - 2 i + 2 \sqrt{3} j$

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