What are the values of the following
`vec(A) xx vec(A)`

Answer

To solve the problem of finding the value of \( \vec{A} \times \vec{A} \), we will utilize the properties of the cross product of vectors.

### Step-by-Step Solution:

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

2. **Identifying the Vectors**:
In this case, we are finding \( \vec{A} \times \vec{A} \). Here, both vectors are the same, meaning:
\[ \vec{A} \text{ and } \vec{A} \text{ are parallel.} \]

3. **Determining the Angle**:
The angle \( \theta \) between \( \vec{A} \) and \( \vec{A} \) is \( 0^\circ \) because they are in the same direction.

4. **Applying the Cross Product Formula**:
Substituting \( \theta = 0^\circ \) into the cross product formula:
\[ \vec{A} \times \vec{A} = |\vec{A}| |\vec{A}| \sin(0^\circ) \hat{n} \]

5. **Calculating the Sine of Zero**:
We know that:
\[ \sin(0^\circ) = 0 \]
Therefore:
\[ \vec{A} \times \vec{A} = |\vec{A}| |\vec{A}| \cdot 0 \cdot \hat{n} = 0 \]

6. **Conclusion**:
Thus, the value of \( \vec{A} \times \vec{A} \) is:
\[ \vec{A} \times \vec{A} = \vec{0} \]

### Final Answer:
\[ \vec{A} \times \vec{A} = \vec{0} \]