`vecA and vecB` are two vectors and `theta` is the angle between them, if `|vecA xx vecB|=sqrt(3)(vecA.vecB)` the value of `theta ` is:-

Options

A. `90^(@)`
B. `60^(@)`
C. `45^(@)`
D. `30^(@)`

Explanation

To solve the problem, we start with the given equation involving the vectors \(\vec{A}\) and \(\vec{B}\):

\[ |\vec{A} \times \vec{B}| = \sqrt{3} (\vec{A} \cdot \vec{B}) \]

### Step 1: Write the expressions for the cross product and dot product
The magnitude of the cross product of two vectors can be expressed as:

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

The dot product of two vectors can be expressed as:

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

### Step 2: Substitute the expressions into the given equation
Now, substituting these expressions into the given equation:

\[ |\vec{A}| |\vec{B}| \sin \theta = \sqrt{3} (|\vec{A}| |\vec{B}| \cos \theta) \]

### Step 3: Cancel out the common terms
Assuming \(|\vec{A}|\) and \(|\vec{B}|\) are not zero, we can divide both sides by \(|\vec{A}| |\vec{B}|\):

\[ \sin \theta = \sqrt{3} \cos \theta \]

### Step 4: Rearrange the equation
We can rearrange the equation to express \(\tan \theta\):

\[ \frac{\sin \theta}{\cos \theta} = \sqrt{3} \]

This simplifies to:

\[ \tan \theta = \sqrt{3} \]

### Step 5: Find the angle \(\theta\)
The angle \(\theta\) that satisfies \(\tan \theta = \sqrt{3}\) is:

\[ \theta = 60^\circ \]

### Final Answer
Thus, the value of \(\theta\) is:

\[ \theta = 60^\circ \]