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 $\overrightarrow{DE}$ is equal to

• 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. $-4\hat{i}-3\hat{j}+2\hat{k}$

Answer 1

Answer: (A)

Given, $\overrightarrow{OA}=4\hat{i}+3\hat{j}-\hat{k}$
$\overrightarrow{OB}=-3\hat{i}+\hat{j}+\hat{k}$
$\therefore$ $\overrightarrow{AB}=\overrightarrow{OB}-\overrightarrow{OA}$
$=-7\hat{i}-2\hat{j}+2\hat{k}$
$\therefore$ $\overrightarrow{DE}=-\overrightarrow{AB}=7\hat{i}+2\hat{j}-2\hat{k}$