The cross product of two vectors gives null vector when the vectors enclose an angle to

Options

A. `90^(@)`
B. `180^(@)`
C. `45^(@)`
D. `120^(@)`

Explanation

To solve the question regarding the conditions under which the cross product of two vectors results in a null vector, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Cross Product**:
The cross product of two vectors **A** and **B** is given by the formula:
\[ \mathbf{A} \times \mathbf{B} = |\mathbf{A}| |\mathbf{B}| \sin(\theta) \hat{n} \]
where \(\theta\) is the angle between the two vectors, and \(\hat{n}\) is the unit vector perpendicular to the plane formed by **A** and **B**.

2. **Condition for Null Vector**:
The cross product results in a null vector (zero vector) when:
\[ \mathbf{A} \times \mathbf{B} = \mathbf{0} \]
This occurs when the entire expression for the cross product equals zero.

3. **Analyzing the Formula**:
From the equation:
\[ |\mathbf{A}| |\mathbf{B}| \sin(\theta) \hat{n} = \mathbf{0} \]
Since **A** and **B** are non-zero vectors, the magnitudes \(|\mathbf{A}|\) and \(|\mathbf{B}|\) are not zero. Therefore, for the product to be zero, we must have:
\[ \sin(\theta) = 0 \]

4. **Finding Angles**:
The sine function equals zero at specific angles:
\[ \sin(\theta) = 0 \quad \text{when} \quad \theta = 0^\circ, 180^\circ, 360^\circ, \ldots \]
Thus, the angles between the vectors that lead to a null vector are \(0^\circ\) and \(180^\circ\).

5. **Conclusion**:
The question specifically asks for the angle that results in a null vector. Among the options provided, the angle \(180^\circ\) is a valid answer. Therefore, the answer to the question is:
\[ \text{The angle is } 180^\circ. \]