Find the distance of the point `2 hat i- hat j-4 hat k` from the plane ` vec rdot((3 hat i-4 hat j+12 hat k)-9=0.`

Explanation

To find the distance of the point \( \vec{a} = 2\hat{i} - \hat{j} - 4\hat{k} \) from the plane given by the equation \( \vec{r} \cdot (3\hat{i} - 4\hat{j} + 12\hat{k}) - 9 = 0 \), we can follow these steps:

### Step 1: Identify the normal vector of the plane
The equation of the plane can be expressed in the form \( \vec{r} \cdot \vec{n} - d = 0 \), where \( \vec{n} \) is the normal vector and \( d \) is a constant. From the given equation, we can identify:
\[ \vec{n} = 3\hat{i} - 4\hat{j} + 12\hat{k} \]
and
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