Find the distance of the point `(-1,-5,-10)` from the point of the intersection of the line `vecr = 2hati-2hatk+lambda(3hati+4hatj+2hatk)` and the plane `vecr.(hati-hatj+hatk) = 5`.

Explanation

To find the distance of the point \((-1, -5, -10)\) from the point of intersection of the given line and plane, we can follow these steps:

### Step 1: Write the equations of the line and the plane.
The equation of the line is given as:
\[ \vec{r} = 2\hat{i} - 2\hat{k} + \lambda(3\hat{i} + 4\hat{j} + 2\hat{k}) \]
This can be rewritten as:
...