If vector `hat(i) - 3hat(j) + 5hat(k)` and `hat(i) - 3 hat(j) - a hat(k)` are equal vectors, then the value of a is :

Options

A. `-5`
B. 2
C. `-3`
D. 4

Answer

To solve the problem, we need to find the value of \( a \) such that the 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**:
The first vector is:
\[ \vec{A} = \hat{i} - 3\hat{j} + 5\hat{k} \]
The second vector is:
\[ \vec{B} = \hat{i} - 3\hat{j} - a\hat{k} \]

2. **Set the vectors equal**:
Since the vectors are equal, we can write:
\[ \hat{i} - 3\hat{j} + 5\hat{k} = \hat{i} - 3\hat{j} - a\hat{k} \]

3. **Compare the components**:
From the equality of the vectors, we can compare the coefficients of \( \hat{k} \):
\[ 5 = -a \]

4. **Solve for \( a \)**:
Rearranging the equation gives:
\[ a = -5 \]

5. **Conclusion**:
The value of \( a \) is:
\[ \boxed{-5} \]