A

Step 1: Understanding the nature of the force and motion. When a particle is moving under the influence of a force that is fixed in both magnitude and direction, the particle experiences a constant force.
Step 2: Analyzing the trajectory. Since the force is constant (both in direction and magnitude), this implies that the acceleration of the particle is also constant. According to Newton's second law, the motion of such a particle will result in a linear path.
Step 3: Conclusion. Hence, the motion of the particle will be in a straight line, as it will continuously accelerate in the direction of the constant force.
Therefore, the correct answer is Option A.