Question

Find the vector Field F whose vector at the point P=(x,y) runs to the line x+y=1.

the solution offered to me was:

I knew that I wanted the gradient to be zero at (0,1) (i.e. have the vectors pointing towards the line y=1-x). Thus I found the gradient, set it equal to zero at that point and solved for the x and y components. I got <1-y, -x>.

is this correct and more importantly HOW do I find the gradient?