question_answer

Let \[\overrightarrow{n}\] be a vector of magnitude \[2\sqrt{3}\] such that it makes equal acute angles with the coordinate axes. Find the vector forms of the equation of a plane passing through \[\left( 1,-1,2 \right)\]and normal to\[\overrightarrow{n}\].

A)  \[\overrightarrow{r}.\,\,(\hat{i}+\hat{j}+\hat{k})=2\]

B)  \[\overrightarrow{r}.\,\,(2\hat{i}+\hat{j}-\hat{k})=2\]

C)  \[\overrightarrow{r}.\,\,(2\hat{i}-\hat{j}-\hat{k})=1\]        

D)  \[\overrightarrow{r}.\,\,(2\hat{i}+3\hat{j}-4\hat{k})=4\]

E)  None of these