The vector equation of the plane which is at a distance of $\frac{3}{\sqrt{14}}$ from the origin and has a normal vector of $2\hat{i} - 3\hat{j} + \hat{k}$ is:

Question

$\vec{r} \cdot (2\hat{i} - 3\hat{j} + \hat{k}) = 3$

$\vec{r} \cdot (\hat{i} + \hat{j} + \hat{k}) = 9$

$\vec{r} \cdot (\hat{i} + 2\hat{j}) = 3$

$\vec{r} \cdot (2\hat{i} + \hat{k}) = 3$

Solution

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