Vector vec(A) points N - E and its magnitude is `3kgms^(-1)` it is multiplied by the scalar `lamda` such that `lamda= - 4` second . Find the magnitude of the new vector quantity.

Options

A. 9
B. 12
C. 19
D. 15

Answer

To solve the problem, we need to find the magnitude of the new vector quantity after multiplying the original vector by a scalar.

### Step-by-Step Solution:

1. **Identify the original vector and its magnitude**:
- The original vector \( \vec{A} \) has a magnitude of \( 3 \, \text{kg m s}^{-1} \).

2. **Identify the scalar**:
- The scalar \( \lambda \) is given as \( -4 \, \text{s} \).

3. **Multiply the vector by the scalar**:
- When a vector is multiplied by a scalar, the magnitude of the new vector \( \vec{A'} \) is given by:
\[ |\vec{A'}| = |\lambda| \times |\vec{A}| \]
- Here, \( |\lambda| = 4 \) (since we are interested in the magnitude, we take the absolute value of the scalar).

4. **Calculate the magnitude of the new vector**:
- Now substituting the values:
\[ |\vec{A'}| = 4 \times 3 \, \text{kg m s}^{-1} = 12 \, \text{kg m s}^{-1} \]

5. **Conclusion**:
- The magnitude of the new vector quantity \( \vec{A'} \) is \( 12 \, \text{kg m s}^{-1} \).

### Final Answer:
The magnitude of the new vector quantity is \( 12 \, \text{kg m s}^{-1} \).