We are not going to go into this in detail but a few simple cases should give you an idea of what is involved. We can describe vectors in terms of lines or arrows, the length and direction of the arrow indicating the magnitude and direction of the vector. Imagine an aeroplane travelling due north at 60m s -1 . This gives us an overall velocity of 75m s -1 . This is where we are going to ease back from the mathematics a little and just look at the simplified case where the second vector is operating perpendicular to our primary vector.
Lets imagine the situation where the wind is blowing due east.
Lets take a look at our plane again. I need to use some mathematics now. We can calculate both the resulting velocity and direction. Velocity using Pythagoras. So our plane has been pushed off course by 14 degrees.