A) \[\overrightarrow{r}.(\hat{i}+\hat{j}+2\hat{k})=1\]
B) \[\overrightarrow{r}.(\hat{i}-\hat{j}+2\hat{k})=1\]
C) \[\overrightarrow{r}.(\hat{i}-\hat{j}+2\hat{k})=7\]
D) \[\overrightarrow{r}.(\hat{i}+\hat{j}-2\hat{k})=10\]
E) None of the above
Correct Answer: B
Solution :
The given line is parallel to the vector \[\overrightarrow{n}=\hat{i}-\hat{j}+2\hat{k}\].The required plane passing through the point\[(2,3,1)\]ie,\[2\hat{i}+3\hat{j}+\hat{k}\]and is perpendicular to the vector \[n=\hat{i}-\hat{j}+2\hat{k}\]. \[\therefore \] Its equation is \[[(\overrightarrow{r}-(2\hat{i}+3\hat{j}+\hat{k})].(\hat{i}-\hat{j}+2\hat{k})=0\] \[\Rightarrow \] \[\overrightarrow{r}.(\hat{i}-\hat{j}+2\hat{k})=1\]
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