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}+\text{ }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} $