Find the shortest distance between lines ` vecr=6 hat i+2 hat j+ hat k+ lambda( hat i-2 hat j+2 hat k)`and ` vecr=-4 hat i- hat k+mu(3 hat i-2 hat j-2 hat k)`.

Explanation

To find the shortest distance between the given lines, we will follow these steps:

### Step 1: Identify the lines in vector form
The first line is given as:
\[ \vec{r_1} = 6 \hat{i} + 2 \hat{j} + \hat{k} + \lambda (\hat{i} - 2\hat{j} + 2\hat{k}) \]
From this, we can identify:
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