In which of the following systeam primitives `a != b != c`?

Options

A. Orthorhombic
B. Monoclinic
C. Triclinic
D. Hexagonal

Answer

To solve the question regarding which crystal systems have the primitive lengths \( a \neq b \neq c \), we will analyze each of the given crystal systems one by one.

### Step-by-Step Solution

1. **Understanding the Crystal Systems**: We need to identify the characteristics of the crystal systems mentioned: Orthorhombic, Monoclinic, Triclinic, and Hexagonal.

2. **Option A: Orthorhombic**
- In an orthorhombic crystal system, the lengths of the axes are different: \( a \neq b \neq c \).
- The angles between the axes are all \( 90^\circ \) (i.e., \( \alpha = \beta = \gamma = 90^\circ \)).
- **Conclusion**: This option satisfies \( a \neq b \neq c \).

3. **Option B: Monoclinic**
- In a monoclinic crystal system, the lengths of the axes can also be different: \( a \neq b \neq c \).
- The angles are such that \( \alpha = \gamma \) (both are \( 90^\circ \)), but \( \beta \) is not equal to \( 90^\circ \).
- **Conclusion**: This option also satisfies \( a \neq b \neq c \).

4. **Option C: Triclinic**
- In a triclinic crystal system, all three lengths are different: \( a \neq b \neq c \).
- Additionally, all angles are also different and not equal to \( 90^\circ \) (i.e., \( \alpha \neq \beta \neq \gamma \)).
- **Conclusion**: This option satisfies \( a \neq b \neq c \).

5. **Option D: Hexagonal**
- In a hexagonal crystal system, the lengths of the axes are such that \( a = b \neq c \).
- The angles are \( \alpha = \beta = 90^\circ \) and \( \gamma = 120^\circ \).
- **Conclusion**: This option does not satisfy \( a \neq b \neq c \).

### Final Answer
The crystal systems that satisfy \( a \neq b \neq c \) are:
- **Option A: Orthorhombic**
- **Option B: Monoclinic**
- **Option C: Triclinic**