A) \[5\hat{i}+\hat{j}-\hat{k}\]
B) \[5\hat{i}+3\hat{j}-3\hat{k}\]
C) \[2\hat{i}+\hat{j}+2\hat{k}\]
D) \[5\hat{i}+\hat{j}+\hat{k}\]
E) \[4\hat{i}+2\hat{j}-2\hat{k}\]
Correct Answer: B
Solution :
\[\overrightarrow{r}=(\hat{i}-\hat{j}+\hat{k})+t(\hat{i}+\hat{j}-\hat{k})\] \[=(1+t)\hat{i}-(1-t)\hat{j}+(1-t)\hat{k}\] Also, \[\overrightarrow{r}.(\hat{i}+\hat{j}+\hat{k})=5\] \[\Rightarrow \] \[(1+t)-(1-t)+(1-t)=5\] \[\Rightarrow \] \[1+t=5\] \[\Rightarrow \] \[t=4\] \[\therefore \] \[\overrightarrow{r}=(1+4)\hat{i}-(1-4)\hat{j}+(1-4)\hat{k}\] \[=5\hat{i}+3\hat{j}-3\hat{k}\]You need to login to perform this action.
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