Which of the following represents a unit vector ?

Options

A. `(|A|)/(A)`
B. `(A)/(|A|)`
C. `(A)/(A)`
D. `(|A|)/(|A|)`

Explanation

To determine which of the given options represents a unit vector, we need to recall the definition of a unit vector. A unit vector is a vector that has a magnitude of 1. It is obtained by dividing a vector by its magnitude.

Let's analyze each option step by step:

1. **Option 1: Magnitude of A divided by vector A**
- This option represents a scalar (the magnitude of vector A) divided by a vector. This does not yield a unit vector. Therefore, this option is incorrect.

2. **Option 2: A vector divided by magnitude of vector A**
- This option represents the vector A divided by its magnitude. Mathematically, this is expressed as:
\[ \text{Unit vector} = \frac{\vec{A}}{|\vec{A}|} \]
- This is the definition of a unit vector, which has a magnitude of 1. Therefore, this option is correct.

3. **Option 3: Vector A divided by vector A**
- This option represents a vector divided by itself. If vector A is not the zero vector, this results in a vector of magnitude 1 in the same direction as A. However, this is not the standard representation of a unit vector. Therefore, this option is incorrect.

4. **Option 4: Magnitude of vector A divided by magnitude of vector A**
- This option results in a scalar value of 1 (since any non-zero number divided by itself is 1). This does not represent a vector, hence it cannot be a unit vector. Therefore, this option is incorrect.

After analyzing all options, we conclude that the only option that correctly represents a unit vector is:

**Correct Answer: Option 2: A vector divided by magnitude of vector A.**