Find the angle between the lines ` -> r=(2 hat i-5 hat j+ hat k)+lambda(3 hat i+2 hat j+6 hat k)a n d\ -> r=7 hat i-6 hat k+mu( hat i+2 hat j+2 hat k)dot`

Explanation

To find the angle between the two lines given by their vector equations, we can follow these steps:

### Step 1: Identify the direction vectors
The first line is given by:
\[ \vec{r} = (2\hat{i} - 5\hat{j} + \hat{k}) + \lambda(3\hat{i} + 2\hat{j} + 6\hat{k}) \]
From this, we can identify the direction vector \(\vec{b_1}\):
...