question_answer

ABCDEF is a regular hexagon where centre O is the origin. If the position vectors of A and B are \[\hat{i}-\hat{j}+2\hat{k}\] and \[2\hat{i}+\hat{j}-\hat{k}\] respectively then \[\overrightarrow{BC}\] is equal to

A) \[\hat{i}+\hat{j}-2\hat{k}\]

B) \[-\hat{i}+\hat{j}-2\hat{k}\]

C) \[3\hat{i}+3\hat{j}-4\hat{k}\]

D) None of these

Correct Answer: B

Solution :

[b] \[\overrightarrow{OA}=\hat{i}-\hat{j}+2\hat{k},\overrightarrow{OB}=2\hat{i}+\hat{j}-\hat{k}\] \[\therefore \,\overrightarrow{OC}=\overrightarrow{AB}=\overrightarrow{OB}-\overrightarrow{OA}=\hat{i}+2\hat{j}-3\hat{k}\] \[\therefore \overrightarrow{BC}=\overrightarrow{OC}-\overrightarrow{OB}=(\hat{i}+2\hat{j}-3\hat{k})-(2\hat{i}+\hat{j}-\hat{k})\] \[=-\hat{i}+\hat{j}-2\hat{k}\]