For the vectors `vecA=hati+2 hat j-hatk and vecB=2 hati+3hatj+2hatk`,
find the vector `vec(AB)` and its magnitude.

Explanation

To solve the problem, we need to find the vector \(\vec{AB}\) and its magnitude, given the vectors \(\vec{A} = \hat{i} + 2\hat{j} - \hat{k}\) and \(\vec{B} = 2\hat{i} + 3\hat{j} + 2\hat{k}\).

### Step 1: Find the vector \(\vec{AB}\)
The vector \(\vec{AB}\) can be found using the formula:
\[ \vec{AB} = \vec{B} - \vec{A} \]

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