A) \[\frac{1}{3}(\hat{i}+2\hat{j}+2\hat{k})\]
B) \[\frac{1}{3}(\hat{i}-2\hat{j}-2\hat{k})\]
C) \[\frac{1}{3}(\hat{i}-2\hat{j}+2\hat{k})\]
D) \[\hat{i}+2\hat{j}+2\hat{k}\]
Correct Answer: A
Solution :
We have,\[\overrightarrow{p}=\hat{i}+\hat{j},\text{ }\overrightarrow{q}=4\hat{k}-\hat{j}\]and \[\overrightarrow{r}=\hat{i}\,2\hat{r}\] \[\therefore \] \[3\overrightarrow{p}+\overrightarrow{q}-2\overrightarrow{r}\] \[=3(\hat{i}+\hat{j})+(4\hat{k}-\hat{j})-2(\hat{i}+\hat{k})\] \[=\hat{i}+2\hat{j}+2\hat{k}\] \[\therefore \]Unit vector of \[3\overrightarrow{p}+\overrightarrow{q}-2\overrightarrow{r}\] \[=\frac{\hat{i}+2\hat{j}+2\hat{k}}{\sqrt{{{1}^{2}}+{{2}^{2}}+{{2}^{2}}}}\] \[=\frac{1}{3}(\hat{i}+2\hat{j}+2\hat{k})\]You need to login to perform this action.
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