If the primary beam area is doubled by opening the collimator, patient dose and exposure to the operator will:

When the primary beam area is doubled by opening the collimator, the dose to the patient and exposure to the operator generally increases due to the larger area being irradiated. However, the relationship between beam area, dose, and exposure doesn't follow a linear pattern.

The intensity of radiation from the beam is related to the area it's covering. When the collimator is adjusted to double the area, the same amount of radiation is spread over a larger surface. This means that while the dose to the patient does increase, it is not increased by a factor of 4 (which would imply that the dose quadruples).

Instead, the increase in beam area results in an increase in exposure proportional to the area—in this case, when the area is doubled, the radiation exposure increases, but because the intensity is also spread over that area, the relationship results in a doubling of exposure rather than a quadruplication or a different factor.

Thus, when the primary beam area is doubled, both patient dose and operator exposure increase by a factor of 2, making the choice correct in this scenario.