ABCDEF be a regular hexagon in the xy plane and AB-=4i‾ , then CD-=

A(0,0) ,B(4,0) ,C(6,23) ⇒ AC =6i+23j AD-=2BC-=4i+43j CD-=AD--AC-=4i+43j-6i-23j =-2i+23j=2(-i+3j)

ABCDEF be a regular hexagon in the xy plane and AB-=4i‾ , then CD-=

A(0,0) ,B(4,0) ,C(6,23) ⇒ AC =6i+23j AD-=2BC-=4i+43j CD-=AD--AC-=4i+43j-6i-23j =-2i+23j=2(-i+3j)

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ABCDEF be a regular hexagon in the xy plane and $\bar{A B} = 4 \overline{i}$ , then $\bar{C D} =$

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

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

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

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

answer is B.

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Detailed Solution

$A (0,0), B (4,0), C (6,2 \sqrt{3}) \overset{}{\Rightarrow AC} = 6 i + 2 \sqrt{3} j \begin{array}{r} \bar{AD} = 2 \bar{BC} = 4 i + 4 \sqrt{3} j \end{array}$
$\bar{CD} = \bar{AD} - \bar{AC} = 4 i + 4 \sqrt{3} j - 6 i - 2 \sqrt{3} j = - 2 i + 2 \sqrt{3} j = 2 (- i + \sqrt{3} j)$