The magnitude of projection of `(2hat(i)-hat(j)+hat(k)) " on" (hat(i)-2hat(j)+2hat(k))` is _____

Explanation

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

\[ \text{Projection of } \mathbf{a} \text{ on } \mathbf{b} = \frac{\mathbf{a} \cdot \mathbf{b}}{|\mathbf{b}|} \]

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

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