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

Options

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

Answer

To solve the problem, we need to determine 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. **Write down the two vectors**:
- Vector 1: \( \hat{i} - 3\hat{j} + 5\hat{k} \)
- Vector 2: \( \hat{i} - 3\hat{j} - a\hat{k} \)

2. **Set the vectors equal to each other**:
\[ \hat{i} - 3\hat{j} + 5\hat{k} = \hat{i} - 3\hat{j} - a\hat{k} \]

3. **Compare the components of the vectors**:
- The \( \hat{i} \) components: \( 1 = 1 \) (this is satisfied)
- The \( \hat{j} \) components: \( -3 = -3 \) (this is also satisfied)
- The \( \hat{k} \) components: \( 5 = -a \)

4. **Solve for \( a \)**:
From the \( \hat{k} \) components, we have:
\[ 5 = -a \]
To find \( a \), multiply both sides by -1:
\[ a = -5 \]

5. **Conclusion**:
The value of \( a \) is \( -5 \).

### Final Answer:
\[ a = -5 \]