$\vec{n}$ is a vector magnitude $2\sqrt{3}$ such that it makes equal angles with coordinate axes. The vector equation of plane passing through (1, -1, 2) and perpendicular to $\vec{n}$ is :
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → $\vec{r}.(\hat{i}+\hat{j}+\hat{k})=2$
$\vec n=2\sqrt{3}(\hat i+\hat j+\hat k)$
makes equal angles with coordinate axes.
let $(\vec a=\hat i-\hat j+2\hat k)$ point on plane
$(\vec r-\vec a).\vec n=0$
$⇒\vec r.\vec n=\vec a.\vec n=2\sqrt{3}$
$\vec r(\hat i+\hat j+\hat k)=2\sqrt{3}(1-1+2)$
$\vec r(\hat i+\hat j+\hat k)=2$