If `vec(P).vec(Q)= PQ`, then angle between `vec(P)` and `vec(Q)` is

Options

A. `0^(@)`
B. `30^(@)`
C. `45^(@)`
D. `60^(@)`

Explanation

To solve the problem, we need to find the angle between the vectors \(\vec{P}\) and \(\vec{Q}\) given that their dot product is equal to the product of their magnitudes.

### Step-by-Step Solution:

1. **Understanding the Dot Product**:
The dot product of two vectors \(\vec{P}\) and \(\vec{Q}\) is given by the formula:
\[ \vec{P} \cdot \vec{Q} = |\vec{P}| |\vec{Q}| \cos \theta \]
where \(\theta\) is the angle between the two vectors.

2. **Setting Up the Equation**:
According to the question, we have:
\[ \vec{P} \cdot \vec{Q} = PQ \]
Here, \(PQ\) represents the product of the magnitudes of vectors \(\vec{P}\) and \(\vec{Q}\). Thus, we can rewrite the equation as:
\[ |\vec{P}| |\vec{Q}| \cos \theta = |\vec{P}| |\vec{Q}| \]

3. **Dividing Both Sides**:
Assuming \(|\vec{P}|\) and \(|\vec{Q}|\) are not zero, we can divide both sides of the equation by \(|\vec{P}| |\vec{Q}|\):
\[ \cos \theta = 1 \]

4. **Finding the Angle**:
The cosine of an angle is equal to 1 when the angle is:
\[ \theta = \cos^{-1}(1) = 0^\circ \]

5. **Conclusion**:
Therefore, the angle between the vectors \(\vec{P}\) and \(\vec{Q}\) is:
\[ \theta = 0^\circ \]