Find the shortest distance between the two lines whose vector equations are given by: `vecr=(1-lamda)hati+(-2lamda -2)hatj+(3-2lamda)hatk and vecr=(1+mu)hati+(2mu-1)hatj-(1+2mu)hatk`

Explanation

To find the shortest distance between the two lines given by their vector equations, we will follow these steps:

### Step 1: Write the vector equations in standard form
The vector equations of the lines are given as:
1. \( \vec{r_1} = (1 - \lambda) \hat{i} + (-2\lambda - 2) \hat{j} + (3 - 2\lambda) \hat{k} \)
2. \( \vec{r_2} = (1 + \mu) \hat{i} + (2\mu - 1) \hat{j} + (-1 + 2\mu) \hat{k} \)

We can express these in the standard form \( \vec{r} = \vec{a} + \lambda \vec{b} \), where \( \vec{a} \) is a point on the line and \( \vec{b} \) is the direction vector.
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