Vector Algebra Question 66
Question: 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
Options:
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
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Answer:
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} $
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