Which one of the following statements concerning vectors and scalars is false ?

Options

A. In calculations, the vector components of a vector may be used in place of the vector itself.
B. It is possible to use vector components that are not perpendicular.
C. A scalar component may be either positive or negative.
D. A vector that is zero may have components other that zero.

Answer

To determine which statement concerning vectors and scalars is false, we need to analyze each of the provided options carefully.

### Step-by-Step Solution:

1. **Understanding Vectors and Scalars**:
- Vectors are quantities that have both magnitude and direction (e.g., displacement, velocity).
- Scalars are quantities that have only magnitude (e.g., temperature, mass).

2. **Analyzing the Statements**:
- We have four statements to evaluate. Let's denote them as A, B, C, and D.

3. **Evaluating Statement A**:
- "The vector component of a vector may be used in place of the vector itself."
- This statement is **true**. A vector can be expressed in terms of its components (e.g., \( \vec{A} = A_x \hat{i} + A_y \hat{j} \)).

4. **Evaluating Statement B**:
- "It is possible to use vector components that are not perpendicular."
- This statement is also **true**. Vector components can be in any direction, not necessarily perpendicular.

5. **Evaluating Statement C**:
- "Scalar components may be either positive or negative."
- This statement is **true**. Scalars can take on any real number value, including negative values.

6. **Evaluating Statement D**:
- "A vector that is zero may have components other than zero."
- This statement is **false**. If a vector is a zero vector (null vector), all its components must also be zero. For example, if \( \vec{A} = 0 \), then \( A_x = 0 \) and \( A_y = 0 \).

7. **Conclusion**:
- The false statement among the options is **Statement D**.

### Final Answer:
The false statement concerning vectors and scalars is: **"A vector that is zero may have components other than zero."**

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