If the angle between the vectors a and b be `theta and a*b=costheta` then the true statement is

Options

A. a and b are equal vectors
B. a and b are like vectors
C. a and b are unlike vectors
D. a and b are unit vectors

Answer

To solve the problem, we start with the given information and analyze it step by step.

### Step 1: Understand the given information
We are given that the angle between two vectors **a** and **b** is θ, and that the dot product of the vectors is given by:
\[ \mathbf{a} \cdot \mathbf{b} = \cos \theta \]

### Step 2: Recall the formula for the dot product
The dot product of two vectors can also be expressed in terms of their magnitudes and the cosine of the angle between them:
\[ \mathbf{a} \cdot \mathbf{b} = |\mathbf{a}| |\mathbf{b}| \cos \theta \]
where \( |\mathbf{a}| \) and \( |\mathbf{b}| \) are the magnitudes (lengths) of vectors **a** and **b**, respectively.

### Step 3: Set up the equation
From the two expressions for the dot product, we can equate them:
\[ |\mathbf{a}| |\mathbf{b}| \cos \theta = \cos \theta \]

### Step 4: Simplify the equation
Assuming \( \cos \theta \neq 0 \) (which means θ is not an odd multiple of π/2), we can divide both sides by \( \cos \theta \):
\[ |\mathbf{a}| |\mathbf{b}| = 1 \]

### Step 5: Analyze the implications
The equation \( |\mathbf{a}| |\mathbf{b}| = 1 \) implies that the product of the magnitudes of vectors **a** and **b** is equal to 1. This means that if both vectors are unit vectors (i.e., their magnitudes are 1), then:
\[ |\mathbf{a}| = 1 \quad \text{and} \quad |\mathbf{b}| = 1 \]

### Conclusion
Thus, the true statement is that both vectors **a** and **b** must be unit vectors. Therefore, the correct option is:
**Both A and B are unit vectors.**

---