Find the projection of `vec(a) = 2 hat(i) - hat(j) + hat(k)` on `vec(b) = hat(i) - 2 hat(j) + hat(k)`.

Explanation

To find the projection of vector \(\vec{a} = 2\hat{i} - \hat{j} + \hat{k}\) on vector \(\vec{b} = \hat{i} - 2\hat{j} + \hat{k}\), we can use the formula for the projection of one vector onto another:

\[ \text{Projection of } \vec{a} \text{ on } \vec{b} = \frac{\vec{a} \cdot \vec{b}}{|\vec{b}|^2} \vec{b} \]

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

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