Final answer:
The phraseology for informing an aircraft that a vector will take it across the final approach course is not provided in the options, but ATC would use precise language, possibly including a phrase like "Crossing final approach course" along with further instructions.
Step-by-step explanation:
The correct phraseology used by air traffic control to inform an aircraft that a vector will take it across the final approach course is not explicitly provided among the options given. However, the terminology used in air traffic control communications is precise and standardized to avoid any confusion. While options such as "Proceed as cleared," "Monitor final approach," and "Caution, vector crossing" convey some measure of information, none of them are standardized phrases for this specific situation. Instead, a controller might say something like: "Crossing final approach course," followed by additional instructions as necessary. It is also possible that ATC could give a vector that takes into account the need to cross the final approach course in combination with an altitude to maintain until a specific point or to expect further clearance.