If `veca,vecb` represent the diagonals of a rhombus, then

Options

A. `vecaxxvecb=0`
B. `veca.vecb=0`
C. `veca.vecb=1`
D. `vecaxxvecb=veca`

Answer

To solve the problem, we need to analyze the properties of the diagonals of a rhombus represented by the vectors \(\vec{A}\) and \(\vec{B}\).

### Step-by-Step Solution:

1. **Understanding the Properties of a Rhombus**:
- A rhombus is a type of quadrilateral where all sides are of equal length.
- One of the key properties of a rhombus is that its diagonals bisect each other at right angles (90 degrees).

2. **Identifying the Angle Between the Diagonals**:
- Since the diagonals of a rhombus intersect at right angles, the angle between the diagonals \(\vec{A}\) and \(\vec{B}\) is \(90^\circ\).

3. **Using the Dot Product Property**:
- The dot product of two vectors \(\vec{A}\) and \(\vec{B}\) is given by the formula:
\[ \vec{A} \cdot \vec{B} = |\vec{A}| |\vec{B}| \cos(\theta) \]
- Here, \(\theta\) is the angle between the two vectors. Since \(\theta = 90^\circ\), we know that:
\[ \cos(90^\circ) = 0 \]
- Therefore, the dot product becomes:
\[ \vec{A} \cdot \vec{B} = |\vec{A}| |\vec{B}| \cdot 0 = 0 \]

4. **Conclusion**:
- Since the dot product of the diagonals \(\vec{A}\) and \(\vec{B}\) is zero, we conclude that:
\[ \vec{A} \cdot \vec{B} = 0 \]

Thus, the correct answer is that the dot product of the diagonals of the rhombus is zero.