Are the following statements true or false? 1. ∇f(a, b) is a vector in 3-dimensional space. 2. If f(x, y) has fx(a, b)=0 and fy(a, b)=0 at the point (a, b), then f is constant everywhere. 3. Suppose fx(a, b) and fy(a, b) both exist. Then there is always a direction in which the rate of change of f at (a, b) is zero. 4. fu⃗ (a, b)=||∇f(a, b)||. 5. If u⃗ is perpendicular to ∇f(a, b), then fu⃗ (a, b)=⟨0,0⟩. 6. If u⃗ is a unit vector, then fu⃗ (a, b) is a vector. 7. fu⃗ (a, b) is parallel to u⃗ . 8. The gradient vector ∇f(a, b) is tangent to the contour of f at (a, b).