Answer:
(17.5√2 miles west, 17.5√2 miles north)
Explanation:
The distance in the west direction will be ...
35cos(45°) = 17.5√2 . . . . miles west
The distance in the north direction will be ...
35sin(45°) = 17.5√2 . . . . miles north
The vector components are ...
(17.5√2 miles west, 17.5√2 miles north)
_____
Additional comment
When a map with the usual "north is up" orientation is overlaid on an x-y coordinate grid, the (x, y) ordered pair directions correspond to (east, north). Using that coordinate meaning for the vector components here, they would be ...
(-24.7, 24.7) miles