By computing the shortest distance determine whether the following pairs of lines intersect or not: ` vec r=( hat i- hat j)+lambda(2 hat i+ hat k)a n d vec r=(2 hat i- hat j)+mu( hat i+ hat j- hat k)`

Explanation

To determine whether the given lines intersect or not, we will compute the shortest distance between them. If the shortest distance is zero, the lines intersect; otherwise, they do not.

### Given Lines:
1. \( \vec{r_1} = (\hat{i} - \hat{j}) + \lambda(2\hat{i} + \hat{k}) \)
2. \( \vec{r_2} = (2\hat{i} - \hat{j}) + \mu(\hat{i} + \hat{j} - \hat{k}) \)

### Step 1: Identify Points and Direction Vectors
From the line equations, we can identify:
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