If `|vecA xx vecB| = vecA.vecB` then the angle between `vecA and vecB` is :

Options

A. 0
B. `pi/4`
C. `pi/2`
D. `pi`

Explanation

To solve the problem, we start with the given equation:

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

### Step 1: Write the expressions for the cross product and dot product.

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

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

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 equate the two expressions:

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

### Step 3: Simplify the equation.

Assuming \(|\vec{A}| \neq 0\) and \(|\vec{B}| \neq 0\), we can divide both sides by \(|\vec{A}| |\vec{B}|\):

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

### Step 4: Solve for \(\theta\).

The equation \(\sin \theta = \cos \theta\) can be rewritten as:

\[ \tan \theta = 1 \]

### Step 5: Find the angle \(\theta\).

The angle \(\theta\) for which \(\tan \theta = 1\) is:

\[ \theta = 45^\circ \]

In radians, this is:

\[ \theta = \frac{\pi}{4} \]

### Conclusion:

Thus, the angle between the vectors \(\vec{A}\) and \(\vec{B}\) is \(45^\circ\) or \(\frac{\pi}{4}\) radians.

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