Find the angel between the vectors ` vec a= hat i- hat j+ hat k\ a n d\ vec b= hat i+ hat j- hat kdot`

Explanation

To find the angle between the vectors \(\vec{a} = \hat{i} - \hat{j} + \hat{k}\) and \(\vec{b} = \hat{i} + \hat{j} - \hat{k}\), we will use the formula:

\[ \cos \theta = \frac{\vec{a} \cdot \vec{b}}{|\vec{a}| |\vec{b}|} \]

### Step 1: Calculate the dot product \(\vec{a} \cdot \vec{b}\)

...