A) \[\overrightarrow{0}\]
B) \[2\overrightarrow{r}\]
C) \[-2\overrightarrow{r}\]
D) \[3\overrightarrow{r}\]
E) none of these
Correct Answer: B
Solution :
Let\[\overrightarrow{r}=x\hat{i}+y\hat{j}+z\hat{k}\] \[\therefore \]\[\hat{i}\times (\overrightarrow{r}\times \hat{i})+\hat{j}\times (\overrightarrow{r}\times \hat{j})+\hat{k}\times (\hat{r}\times \hat{k})\] \[=(\hat{i}.\hat{i})\overrightarrow{r}-(\hat{i}.\overrightarrow{r})\hat{i}+(\hat{j}.\hat{j})\overrightarrow{r}-(\hat{j}.\overrightarrow{r})\hat{j}\] \[+(\hat{k}.\hat{k})\overrightarrow{r}-(\hat{k}-\overrightarrow{r})\hat{k}\] \[=3\overrightarrow{r}-(x\hat{i}+y\hat{j}+z\hat{k})\] \[=3\overrightarrow{r}-\overrightarrow{r}\] \[=2\overrightarrow{r}\]You need to login to perform this action.
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