If `vec(a) = hat(i) + hat(j) + 2 hat(k)` and `vec(b) = 3 hat(i) + 2 hat(j) - hat(k)`, find the value of`(vec(a) + 3 vec(b))`. `( 2 vec(a) - vec(b))`.

Explanation

To solve the problem, we need to compute the expression \((\vec{a} + 3\vec{b}) \cdot (2\vec{a} - \vec{b})\) using the given vectors \(\vec{a}\) and \(\vec{b}\).

### Step 1: Write down the vectors
Given:
\[ \vec{a} = \hat{i} + \hat{j} + 2\hat{k} \]
\[
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