If vector `hati- 3hatj+5hatk and hati-3hatj-ahatk` are equal vector then find the value of a.

Explanation

To solve the problem, we need to find the value of \( a \) such that the two vectors \( \hat{i} - 3\hat{j} + 5\hat{k} \) and \( \hat{i} - 3\hat{j} - a\hat{k} \) are equal.

### Step-by-Step Solution:

1. **Identify the vectors**:
Let vector \( \mathbf{A} = \hat{i} - 3\hat{j} + 5\hat{k} \) and vector \( \mathbf{B} = \hat{i} - 3\hat{j} - a\hat{k} \).

2. **Set the vectors equal**:
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