**Kinematic Indeterminacy of a Pin-Jointed Space Frame**

In structural analysis, the kinematic indeterminacy of a structure refers to the number of additional unknown displacements or rotations that are required to fully determine the internal forces and deformations within the structure. For a pin-jointed space frame, the kinematic indeterminacy can be determined using the equation:

**Degree of Kinematic Indeterminacy = 3J - R**

Where:
- J = Number of Joints in the structure
- R = Number of Reaction components or supports

Let's understand why the correct answer is option 'B' by breaking down the equation and explaining each term:

**Degree of Kinematic Indeterminacy = 3J - R**

1. **Joints (J):** Joints in a pin-jointed space frame are the locations where two or more members meet and are connected by pins or hinges. The number of joints is denoted by the variable J.

2. **Reaction Components (R):** Reaction components refer to the number of support reactions at the supports or fixed points of the structure. These can include vertical, horizontal, and moment reactions. The number of reaction components is denoted by the variable R.

The equation suggests that the degree of kinematic indeterminacy is equal to three times the number of joints minus the number of reaction components.

**Explanation:**

1. The factor of 3 in the equation is due to the three degrees of freedom (displacements or rotations) at each joint in a pin-jointed space frame. These three degrees of freedom can be classified as vertical displacement, horizontal displacement, and rotation.

2. The term 3J represents the total number of unknown displacements and rotations at all the joints in the structure. This is because each joint has three degrees of freedom.

3. The term R represents the number of reaction components or supports. These supports restrict the displacements and rotations at certain points in the structure, reducing the overall degree of kinematic indeterminacy.

Therefore, the correct equation for the degree of kinematic indeterminacy of a pin-jointed space frame is given by:

**Degree of Kinematic Indeterminacy = 3J - R**

Hence, the correct answer is option 'B' (3J - R).