If `veca and vecb` are two nonzero vectors such that `|vecaxxvecb|=veca.vecb` then find the angle between `veca and vecb.`

Answer

To solve the problem, we need to find the angle between two nonzero vectors \(\vec{a}\) and \(\vec{b}\) given the condition that the magnitude of their cross product is equal to their dot product.

### Step-by-Step Solution:

1. **Understanding the Given Condition**:
We are given that:
\[ |\vec{a} \times \vec{b}| = \vec{a} \cdot \vec{b} \]

2. **Using the Formulas for Cross Product and Dot Product**:
We know the formulas for the magnitudes of the cross product and the dot product:
- The magnitude of the cross product:
\[ |\vec{a} \times \vec{b}| = |\vec{a}| |\vec{b}| \sin \theta \]
- The dot product:
\[ \vec{a} \cdot \vec{b} = |\vec{a}| |\vec{b}| \cos \theta \]

3. **Setting the Two Expressions Equal**:
Now, substituting these formulas into the given condition:
\[ |\vec{a}| |\vec{b}| \sin \theta = |\vec{a}| |\vec{b}| \cos \theta \]

4. **Dividing Both Sides by \(|\vec{a}| |\vec{b}|\)**:
Since \(\vec{a}\) and \(\vec{b}\) are nonzero vectors, we can safely divide both sides by \(|\vec{a}| |\vec{b}|\):
\[ \sin \theta = \cos \theta \]

5. **Using the Identity**:
The equation \(\sin \theta = \cos \theta\) can be rewritten using the tangent function:
\[ \tan \theta = 1 \]

6. **Finding the Angle**:
The angle \(\theta\) for which \(\tan \theta = 1\) is:
\[ \theta = \frac{\pi}{4} \text{ radians} \quad \text{or} \quad 45^\circ \]

### Final Answer:
The angle between the vectors \(\vec{a}\) and \(\vec{b}\) is:
\[ \theta = 45^\circ \quad \text{or} \quad \frac{\pi}{4} \text{ radians} \]