Find the shortest distance between lines `vecr = 6hati+2hatj+2hatk+lambda(hati-2hatj+2hatk)` and `vecr = -4hati-hatk +mu(3hati-2hatj-2hatk)`.

Explanation

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

### Step 1: Identify the vectors
The equations of the lines are given as:
1. Line 1: \(\vec{r_1} = 6\hat{i} + 2\hat{j} + 2\hat{k} + \lambda(\hat{i} - 2\hat{j} + 2\hat{k})\)
2. Line 2: \(\vec{r_2} = -4\hat{i} - \hat{k} + \mu(3\hat{i} - 2\hat{j} - 2\hat{k})\)

From these equations, we can identify:
...