Find the projection of the vector ` hat i+3 hat j+7 hat k` on the vector `2 hat i-3 hat j+6 hat kdot`

Explanation

To find the projection of the vector \( \mathbf{a} = \hat{i} + 3\hat{j} + 7\hat{k} \) on the vector \( \mathbf{b} = 2\hat{i} - 3\hat{j} + 6\hat{k} \), we can use the formula for the projection of vector \( \mathbf{a} \) onto vector \( \mathbf{b} \):

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

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

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