If `|vecA xx vecB| = |vecA*vecB|`, then the angle between `vecA and vecB` will be :

Options

A. `30^(@)`
B. `45^(@)`
C. `60^(@)`
D. `75^(@)`

Explanation

To solve the problem, we need to analyze the given condition:

\[ |\vec{A} \times \vec{B}| = |\vec{A} \cdot \vec{B}| \]

### Step 1: Write the expressions for the magnitudes of the cross product and dot product.
The magnitude of the cross product of two vectors \(\vec{A}\) and \(\vec{B}\) is given by:

\[ |\vec{A} \times \vec{B}| = |\vec{A}| |\vec{B}| \sin \theta \]

where \(\theta\) is the angle between the two vectors.

The magnitude of the dot product of two vectors \(\vec{A}\) and \(\vec{B}\) is given by:

\[ |\vec{A} \cdot \vec{B}| = |\vec{A}| |\vec{B}| \cos \theta \]

### Step 2: Set the two expressions equal to each other.
From the problem statement, we have:

\[ |\vec{A}| |\vec{B}| \sin \theta = |\vec{A}| |\vec{B}| \cos \theta \]

### Step 3: Simplify the equation.
Assuming \(|\vec{A}|\) and \(|\vec{B}|\) are not zero, we can divide both sides by \(|\vec{A}| |\vec{B}|\):

\[ \sin \theta = \cos \theta \]

### Step 4: Use the identity to find the angle.
The equation \(\sin \theta = \cos \theta\) can be rewritten in terms of tangent:

\[ \tan \theta = 1 \]

### Step 5: Solve for \(\theta\).
The angle \(\theta\) that satisfies \(\tan \theta = 1\) is:

\[ \theta = 45^\circ \]

### Conclusion:
Thus, the angle between vectors \(\vec{A}\) and \(\vec{B}\) is \(45^\circ\).