Find the value of n such that the vectors `4 hat(i) + 3hat(j) - 7hat(k) and 5 hat(i) + 2hat(j) - nhat(k)` may be orthogonal .

Explanation

To find the value of \( n \) such that the vectors \( \mathbf{A} = 4 \hat{i} + 3 \hat{j} - 7 \hat{k} \) and \( \mathbf{B} = 5 \hat{i} + 2 \hat{j} - n \hat{k} \) are orthogonal, we will use the property that the dot product of two orthogonal vectors is zero.

### Step-by-Step Solution:

1. **Understand Orthogonality**:
Two vectors are orthogonal if their dot product equals zero.

2. **Write the Vectors**:
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