tangent vector field G = Pi + Q: x^2 + y^2 = a^2 + b^2

[cheffy]

Find a field G=P(x,y)i +Q(x,y)j in the xy-plane with the property that at any point \(\displaystyle (a,b) \ne (0,0)\), G is a unit vector tangent to the circle \(\displaystyle x^2 + y^2 = a^2 + b^2\) and pointing in the clockwise direction.

I have no clue how to do this. Help please.

 

[Unco]

A circle, centre (0,0), with radius r traced clockwise can be parameterised via (x,y) = (r*cos(-t), r*sin(-t)) = (r*cos(t), -r*sin(t)); 0<=t<2*pi. The tangent vector is then (-r*sin(t), -r*cos(t)) = (y, -x). All that is left is to normalise it.