Find the angle between the pair of lines given by ` vecr=3 hat i+2 hat j-4 hat k+lambda( hat i+2 hat j+2 hat k)`and` vecr=5 hat i-2 hat j+mu(3 hat i+2 hat j+6 hat k)`.

Explanation

To find the angle between the given pair of lines, we can use the formula for the cosine of the angle between two lines represented in vector form. The lines are given as:

1. \(\vec{r_1} = 3\hat{i} + 2\hat{j} - 4\hat{k} + \lambda(\hat{i} + 2\hat{j} + 2\hat{k})\)
2. \(\vec{r_2} = 5\hat{i} - 2\hat{j} + \mu(3\hat{i} + 2\hat{j} + 6\hat{k})\)

### Step 1: Identify Direction Vectors
From the equations of the lines, we can identify the direction vectors:
- For the first line, the direction vector \(\vec{b_1} = \hat{i} + 2\hat{j} + 2\hat{k}\).
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