If vectors `2hati - 3hatj-5hatk and 2hati-3 hatj-ahatk` are equal vectors,  then the value of a is

Options

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

Answer

To find the value of \( a \) such that the vectors \( 2\hat{i} - 3\hat{j} - 5\hat{k} \) and \( 2\hat{i} - 3\hat{j} - a\hat{k} \) are equal, we can follow these steps:

### Step 1: Write down the vectors
We have two vectors:
- Vector A: \( \vec{A} = 2\hat{i} - 3\hat{j} - 5\hat{k} \)
- Vector B: \( \vec{B} = 2\hat{i} - 3\hat{j} - a\hat{k} \)

### Step 2: Set the vectors equal to each other
Since the vectors are equal, we can write:
\[ \vec{A} = \vec{B} \]

### Step 3: Compare the coefficients of \( \hat{i}, \hat{j}, \hat{k} \)
From the equality of the vectors, we can equate the coefficients of \( \hat{i}, \hat{j}, \hat{k} \):
1. Coefficient of \( \hat{i} \): \( 2 = 2 \) (This is already satisfied)
2. Coefficient of \( \hat{j} \): \( -3 = -3 \) (This is also satisfied)
3. Coefficient of \( \hat{k} \): \( -5 = -a \)

### Step 4: Solve for \( a \)
From the equation \( -5 = -a \), we can multiply both sides by -1:
\[ 5 = a \]

### Conclusion
Thus, the value of \( a \) is \( 5 \).

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