Which of the following is a null vector
(a) velocity vector of a body moving in a circle with a uniform speed
(b) velocity vector of a body moving in a straight line with a uniform speed
(c) position vector of the origin of the rectangular coordinate system
(d) displacement vector of a stationary object

Options

A. both a & b
B. both b & c
C. a, b & c
D. both c & d

Answer

To determine which of the given options is a null vector, we need to understand what a null vector is. A null vector, also known as a zero vector, is a vector that has a magnitude of zero and does not have any specific direction.

Let's analyze each option step by step:

1. **Option (a): Velocity vector of a body moving in a circle with uniform speed.**
- A body moving in a circle with uniform speed has a constant speed but is continuously changing direction. Therefore, the velocity vector is not zero; it has a specific magnitude (the speed) and a direction (the tangent to the circle at any point).
- **Conclusion:** This is not a null vector.

2. **Option (b): Velocity vector of a body moving in a straight line with uniform speed.**
- A body moving in a straight line with uniform speed also has a constant speed and a specific direction. The velocity vector has a non-zero magnitude equal to the speed of the body.
- **Conclusion:** This is not a null vector.

3. **Option (c): Position vector of the origin of the rectangular coordinate system.**
- The position vector of the origin (0, 0) in a rectangular coordinate system is represented as (0, 0). Since the magnitude of this vector is zero, it qualifies as a null vector.
- **Conclusion:** This is a null vector.

4. **Option (d): Displacement vector of a stationary object.**
- A stationary object does not change its position, meaning its displacement is zero. Therefore, the displacement vector also has a magnitude of zero.
- **Conclusion:** This is a null vector.

After analyzing all the options, we find that both option (c) and option (d) are null vectors.

**Final Answer:** The null vectors are (c) position vector of the origin of the rectangular coordinate system and (d) displacement vector of a stationary object.