Find the projection of the vector ` hat i+3 hat j+7 hat k`on the vector `7 hat i- hat j+8 hat k`

Explanation

To find the projection of the vector \(\mathbf{A} = \hat{i} + 3\hat{j} + 7\hat{k}\) on the vector \(\mathbf{B} = 7\hat{i} - \hat{j} + 8\hat{k}\), we will follow these steps:

### Step 1: Calculate the dot product \(\mathbf{A} \cdot \mathbf{B}\)

The dot product of two vectors \(\mathbf{A} = a_1\hat{i} + a_2\hat{j} + a_3\hat{k}\) and \(\mathbf{B} = b_1\hat{i} + b_2\hat{j} + b_3\hat{k}\) is given by:

\[
\mathbf{A} \cdot \mathbf{B} = a_1b_1 + a_2b_2 + a_3b_3
...