If `|vec P xx vec Q|=PQ` then the angle between `vec P and vec Q` is

Options

A. zero
B. `90^(@)`
C. `45^(@)`
D. any angle between 0 and `180^(@)`

Explanation

To solve the problem, we need to find the angle between the vectors \( \vec{P} \) and \( \vec{Q} \) given that \( |\vec{P} \times \vec{Q}| = PQ \).

### Step-by-Step Solution:

1. **Understanding the Cross Product**:
The magnitude of the cross product of two vectors \( \vec{P} \) and \( \vec{Q} \) is given by the formula:
\[ |\vec{P} \times \vec{Q}| = |\vec{P}| |\vec{Q}| \sin \theta \]
where \( \theta \) is the angle between the two vectors.

2. **Setting Up the Equation**:
According to the problem, we have:
\[ |\vec{P} \times \vec{Q}| = PQ \]
where \( P = |\vec{P}| \) and \( Q = |\vec{Q}| \).

3. **Substituting the Magnitudes**:
Substitute the expression for the magnitude of the cross product into the equation:
\[ |\vec{P}| |\vec{Q}| \sin \theta = PQ \]

4. **Simplifying the Equation**:
Since \( P = |\vec{P}| \) and \( Q = |\vec{Q}| \), we can rewrite the equation as:
\[ PQ \sin \theta = PQ \]

5. **Dividing Both Sides**:
Divide both sides of the equation by \( PQ \) (assuming \( P \) and \( Q \) are not zero):
\[ \sin \theta = 1 \]

6. **Finding the Angle**:
The sine of an angle is equal to 1 when the angle is:
\[ \theta = 90^\circ \]

### Conclusion:
Thus, the angle between the vectors \( \vec{P} \) and \( \vec{Q} \) is \( 90^\circ \).