What happens, when we multiply a vector by `(-2)`

Options

A. direction reverses and unit changes
B. direction reverses and magnitude gets changes
C. direction remains unchanged and unit changes
D. none of the above

Explanation

To solve the question of what happens when we multiply a vector by \(-2\), let's break it down step by step:

### Step 1: Understand Vector Multiplication
A vector is a quantity that has both magnitude and direction. When we multiply a vector by a scalar (a real number), we affect its magnitude and possibly its direction.

### Step 2: Define the Vector
Let’s denote the vector as \(\mathbf{A}\). The vector can be represented in terms of its magnitude and direction.

### Step 3: Multiply the Vector by \(-2\)
When we multiply the vector \(\mathbf{A}\) by \(-2\), we get:
\[ \mathbf{B} = -2\mathbf{A} \]

### Step 4: Analyze the Result
1. **Magnitude Change**: The magnitude of the vector \(\mathbf{A}\) is multiplied by \(-2\). The magnitude of \(\mathbf{B}\) becomes:
\[ |\mathbf{B}| = |-2| \cdot |\mathbf{A}| = 2 |\mathbf{A}| \]
This means the magnitude of the vector doubles.

2. **Direction Change**: The negative sign indicates that the direction of the vector is reversed. If \(\mathbf{A}\) points in a certain direction, \(\mathbf{B}\) will point in the opposite direction.

### Step 5: Conclusion
When a vector is multiplied by \(-2\):
- The magnitude of the vector changes (it doubles in this case).
- The direction of the vector is reversed.

Thus, the correct answer to the question is that the direction reverses and the magnitude changes.

### Final Answer
The correct option is: **Direction reverses and magnitude gets changed.**

---