Which of the following statements is incorrect? a) Path length is a scalar quantity whereas displacement is a vector quantity. b) The displacement depends only on the end points whereas path length depends on the actual path followed. c) The path length is always positive whereas displacement can be positive, negative and zero. d) The path length is always positive whereas displacement can be positive, negative and zero.

Options

A. Path length is a scalar quantity whereas displacement is a vector quantity.
B. The displacement depends only on the end points whereas path length depends on the actual path followed.
C. The path length is always positive whereas displacement can be positive, negative and zero.
D. The path length is always positive whereas displacement can be positive, negative and zero.

Explanation

To determine which statement is incorrect, let's analyze each option one by one.

### Step 1: Analyze Statement A
**Statement A:** "Path length is a scalar quantity whereas displacement is a vector quantity."

- **Explanation:** Path length refers to the total distance traveled regardless of direction, making it a scalar quantity (only magnitude). Displacement, on the other hand, is defined as the change in position and includes both magnitude and direction, making it a vector quantity.
- **Conclusion:** This statement is correct.

### Step 2: Analyze Statement B
**Statement B:** "The displacement depends only on the end points whereas path length depends on the actual path followed."

- **Explanation:** Displacement indeed depends on the initial and final positions (end points) and does not consider the path taken. However, the statement implies that path length is independent of the end points, which is misleading. Path length is the total distance traveled and does depend on the actual path taken.
- **Conclusion:** This statement is misleading and incorrect.

### Step 3: Analyze Statement C
**Statement C:** "The path length is always positive whereas displacement can be positive, negative and zero."

- **Explanation:** Path length is always a positive quantity since it measures distance. Displacement can be positive (moving in the positive direction), negative (moving in the opposite direction), or zero (returning to the starting point).
- **Conclusion:** This statement is correct.

### Step 4: Analyze Statement D
**Statement D:** "The path length is always positive whereas displacement can be positive, negative and zero."

- **Explanation:** This statement is identical to Statement C and is also true for the same reasons.
- **Conclusion:** This statement is correct.

### Final Conclusion
The incorrect statement among the options provided is **Statement B**.