ok to normalize a vector
divide its x,y by its length
the vector in our example is -5,5 (vector towards target from player)
length = sqr( (-5 * 5) + (5 * 5))
length = sqr ( 25 + 25)
length = sqr (50)
length = 7.07
didn't you make a mistake in your magnitude calculation? since the brackets must be added before you find the square root?
normalized = -5/7.07 = -0.7
5/7.07 = 0.7
This is the cosine of the angle between you, and cos(90degrees) = 0, so they are perpendicular to your facing.
now that part I do not get. Could you word that better?