find plot it on the level surface of f that passes through
and is a plane passing through
find intercepts and draw then plot from (0,0,1) the vector <-1,1,1>
??
A "level surface" for f(x,y,z) is a surface on which f(x,y,z)= C for some constant C. For f(x)= z- x+ y, you are correct, that will be a plane: z- x+ y= C. And, of course, (0, 0, 1) satisfies 1- 0+ 0= 1 so the level surface containing (0, 0, 1) is the plane z- x+ y= 1. Yes, grad f, at (0, 0, 1) is <-1, 1, 1> which does NOT lie in the plane z- x+ y= 1. So I don't know what this question is asking! Perhaps it means the projection of the vector on that plane.