Plz answer each of them thanks so much !

10. Are the following statements true or false? a. If u is a unit vector, then f.(a, b) is a vector. b. If u is perpendicular to V f(a, b), then fa (a, b) = (0, 0). c. Suppose fr(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. d. If f(x, y) has f=(a, b) - 0 and fy(a, b) - 0 at the point (a, b), then f is constant everywhere. e. Vf(a, b) is a vector in 3-dimensional space. f. fa (a, b) - |IVf(a, b)Il. g. The gradient vector Vf(a, b) is tangent to the contour of f at (a, b). h. fa (a, b) is parallel to u. Make Interactive 14. Let f(z, y) - 2 + 3y. a. Find Vf(z, y) and V f(1, 2). b. Find the direction of greatest increase in f at the point (1, 2). Explain. A graph of the surface defined by f is shown at left in Figure 10.6.7. Illustrate this direction on the surface. C. A contour diagram of f is shown at right in Figure 10.6.7 . Illustrate your calculation from (b) on this contour diagram. Gin 40 20 Figure 10.6.7. Left: Graph of f(z, y) = 13 + 3y. Right: Contours. d. Find a direction w for which the derivative of f in the direction of w is zero