Give a formula $F=M(x,y)i + N(x,y)j$ for the vector field in the plane that has the property that F points toward the origin with magnitude inversely proportional to the square of the distance from (x,y) to the origin. (The field is not defined at (0,0)).
I first found the norm of the vector $|F|=k/(x^2+y^2)$ with k>0.
Then I set $F=|F|n$ with n being the direction of the vector F. I put $n=(-x)i+(-y)j$ but the solution manual set $n=(-x/\sqrt{x^2+y^2})i+(-y/\sqrt{x^2+y^2})j$ and I don't understand why.
$n$ should be so that $||n||= 1$