Question

A, B, C, D, E, F in that order, are the vertices of a regular hexagon with centre origin. If the position vectors of the vertices A and B are, respectively $4\hat{i}+3\hat{j}-\hat{k}$ and $-3\hat{i}+\hat{j}+\hat{k}\,then\,\overrightarrow{DE}=$

• A. $7\hat{i}+2\hat{j}-2\hat{k}$
• B. $-7\hat{i}-2\hat{j}+2\hat{k}$
• C. $3\hat{i}-\hat{j}-\hat{k}$
• D. $-4\hat{i}-3\hat{j}+\hat{k}$

Answer 1

Answer: (A)

$\overline{DE}=\overline{BA}$

$=\left(4\,\hat{i}+3\,\hat{j}-\hat{k}\right)-3\left(-3\,\hat{i}+\hat{j}+\hat{k}\right)$
$=7\,\hat{i}+2\,\hat{j}-2\,\hat{k}$