Find the distance of the point `( 1, 5, 10)`from the point of intersection of the line ` -> r=2 hat i- hat j+2 hat k+lambda(3 hat i+4 hat j+2 hat k)`and the plane ` -> r=( hat i- hat j+ hat k)=5`.

Explanation

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

### Step 1: Write the equation of the line and the plane

The equation of the line is given as:
\[ \vec{r} = 2\hat{i} - \hat{j} + 2\hat{k} + \lambda(3\hat{i} + 4\hat{j} + 2\hat{k}) \]
...