If any two of three vectors `vec(a), vec(b), vec(c )` are parallel, then `[vec(a)vec(b)vec(c )]=` __________.

Answer

To solve the problem, we need to determine the value of the scalar triple product \([ \vec{a} \, \vec{b} \, \vec{c} ]\) given that any two of the three vectors \(\vec{a}, \vec{b}, \vec{c}\) are parallel.

### Step-by-Step Solution:

1. **Understanding Parallel Vectors**:
If two vectors are parallel, it means they point in the same direction or in exactly opposite directions. For example, if \(\vec{b}\) and \(\vec{c}\) are parallel, then we can express this as \(\vec{b} = k \vec{c}\) for some scalar \(k\).

2. **Scalar Triple Product Definition**:
The scalar triple product \([ \vec{a} \, \vec{b} \, \vec{c} ]\) is defined as:
\[ [ \vec{a} \, \vec{b} \, \vec{c} ] = \vec{a} \cdot (\vec{b} \times \vec{c}) \]
where \(\vec{b} \times \vec{c}\) is the cross product of \(\vec{b}\) and \(\vec{c}\).

3. **Cross Product of Parallel Vectors**:
If \(\vec{b}\) and \(\vec{c}\) are parallel, the angle \(\theta\) between them is either \(0\) or \(180\) degrees. In both cases, the sine of the angle is:
\[ \sin(0) = 0 \quad \text{and} \quad \sin(180) = 0 \]
Therefore, the magnitude of the cross product \(\vec{b} \times \vec{c}\) is:
\[ |\vec{b} \times \vec{c}| = |\vec{b}| |\vec{c}| \sin(\theta) = 0 \]
This implies:
\[ \vec{b} \times \vec{c} = \vec{0} \]

4. **Substituting into the Scalar Triple Product**:
Now substituting back into the scalar triple product:
\[ [ \vec{a} \, \vec{b} \, \vec{c} ] = \vec{a} \cdot (\vec{b} \times \vec{c}) = \vec{a} \cdot \vec{0} = 0 \]

5. **Conclusion**:
Thus, if any two of the three vectors \(\vec{a}, \vec{b}, \vec{c}\) are parallel, the value of the scalar triple product is:
\[ [ \vec{a} \, \vec{b} \, \vec{c} ] = 0 \]

### Final Answer:
\[ [ \vec{a} \, \vec{b} \, \vec{c} ] = 0 \]