A vector is a magnitude and direction. An airplane has its speed and direction (a vector). The wind also has a speed and direction (a vector).

A general solution to the problem is

1. calculate the wind and airplane speeds (velocities) independently
2. break each of them into independent (orthogonal) vectors
3. add (or subtract) the independent vectors
4. combine the resulting independent vectors back into a single vector
5. you now know the airplane's actual speed and direction (velocity)