An expression which cannot be defined meaningfully among vectors is :

Options

A. `vecA.(vecB xx vecC)`
B. `vecAxx(vecB xx vecC)`
C. `(vecA xx vecB)xx(vecC xx vecD)`
D. `(vecA . vecB)xx(vecC . vecD)`

Explanation

To solve the question of which expression cannot be defined meaningfully among vectors, we will analyze each option based on the properties of vector operations.

### Step-by-Step Solution:

1. **Understand Vector Operations**:
- There are two primary operations for vectors: the dot product and the cross product.
- The dot product of two vectors results in a scalar.
- The cross product of two vectors results in another vector.

2. **Evaluate Each Expression**:
- **Expression 1: A · (B × C)**
- Here, B × C is a vector.
- A · (B × C) is a dot product of vector A and the resulting vector from B × C, which is a scalar.
- This expression is meaningful.

- **Expression 2: A × (B × C)**
- B × C is a vector.
- A × (B × C) is a cross product of vector A and the resulting vector from B × C, which is also a vector.
- This expression is meaningful.

- **Expression 3: (A × B) × C**
- A × B is a vector.
- (A × B) × C is a cross product of the vector (A × B) and vector C, resulting in another vector.
- This expression is meaningful.

- **Expression 4: A · B**
- A · B is a dot product of two vectors A and B, resulting in a scalar.
- However, if we consider the expression A × B (cross product), it results in a vector.
- The dot product of two vectors is defined, but the cross product of scalars is not defined.
- Therefore, this expression cannot be defined meaningfully.

3. **Conclusion**:
- The expression that cannot be defined meaningfully among vectors is **A · B** when considering it in the context of cross products, as you cannot perform a cross product operation on scalars.

### Final Answer:
The expression which cannot be defined meaningfully among vectors is **A · B**.