A vector multiplied by the number 0, results into

Options

A. 0
B. `vecA`
C. `vec0`
D. `vecA`

Answer

To solve the question, "A vector multiplied by the number 0 results into," we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Vector**:
Let's denote the vector as **A**. In component form, we can express it as:
\[ \mathbf{A} = A_x \hat{i} + A_y \hat{j} + A_z \hat{k} \]
where \(A_x\), \(A_y\), and \(A_z\) are the components of the vector along the x, y, and z axes, respectively.

2. **Multiplying the Vector by Zero**:
When we multiply the vector **A** by 0, we perform the operation on each component:
\[ \mathbf{A} \cdot 0 = (A_x \hat{i} + A_y \hat{j} + A_z \hat{k}) \cdot 0 \]
This can be expanded as:
\[ = A_x \cdot 0 \hat{i} + A_y \cdot 0 \hat{j} + A_z \cdot 0 \hat{k} \]

3. **Calculating Each Component**:
Since any number multiplied by 0 is 0, we have:
\[ A_x \cdot 0 = 0, \quad A_y \cdot 0 = 0, \quad A_z \cdot 0 = 0 \]

4. **Resulting Vector**:
Therefore, the resulting vector after multiplying by 0 is:
\[ = 0 \hat{i} + 0 \hat{j} + 0 \hat{k} \]
This simplifies to:
\[ \mathbf{0} = \mathbf{0} \hat{i} + \mathbf{0} \hat{j} + \mathbf{0} \hat{k} \]
which is known as the **null vector** or **zero vector**.

5. **Conclusion**:
Thus, we conclude that multiplying any vector by 0 results in the zero vector.

### Final Answer:
A vector multiplied by the number 0 results in the **zero vector** (or **null vector**).

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