a is correct
14. A vector that is normal to the graph of 2 - x² + y2 +7 at the point (2,1,12) is a)4î +29 - † b) i-29 +3k c) 7 + i +4 d) - 6 - 29 + Ře) none of these
3. (a) Consider the paraboloid z = x2 + y2 Find a unit vector normal to the surface of this paraboloid at the point P = (x, y, z) = (1, 2,5). (b) Consider a vector field ä = (xy2 + z)i + (xy + 2)9 + xk where, as usual, i = Î. Ì = û and k = 2 are the unit vectors. Show that a = Vº for some scalar field o.
4- Find the slope of f(x, y, z) = D. Inz + 50e + yºz at P(1,0,-1) along the vector v = 4i - 2j + 4k a) 7 -2.17 b) 2.33 C) -4 3 e) 0.92 KÖnceki 4/4 Sonraki Kapat ✓ Sınavı Biti
6. Consider the vector field F = (x + sin y) î + y²z + x2 î. (a) Compute the divergence of for the point (2, -3,1). (7 points) (b) Consider F as the velocity field for fluid flow. Imagine a small drop of dye placed at the point (2, -3,1). Describe how the volume of the drop will change (instanta- neously) as the dye particles move with the flow. (3 points) (c) Compute the curl of F for the...
a=4i + k Calculate the vector product axb Check that a x b is normal to a and to b Calculate exd and lexd Find a unit vector normal to the plane of the vectors b and d b- 2i-3j-k d--i+2j+k
The directional derivative of a function f(x, y, z) = 2x²yz - 100 at the point Po(1,-1,-1) in the direction of a vector v = 2i + 2j + k is Select one: 2 A. 3 B. 2 C. D.O. E. None of these answers
Consider the vector field F(x, y, z) -(z,2x, 3y) and the surface z- /9 - x2 -y2 (an upper hemisphere of radius 3). (a) Compute the flux of the curl of F across the surface (with upward pointing unit normal vector N). That is, compute actually do the surface integral here. V x F dS. Note: I want you to b) Use Stokes' theorem to compute the integral from part (a) as a circulation integral (c) Use Green's theorem (ie...
Find a vector perpendicular to both 7 = 2î + +5k and w=4ỉ – 2j+k a) 3î +79-6 b) 1lî +189 – sł c) 4 -8j+ť d){+99–3 e) none of these
ite 9) Vector A has x component Ax = -10.0 m. Ã makes an angle of 32.0° clockwise from the-y axis. wne d silt ahal B = -2.00 m î + 6.00 m j – 3.00 m k, and C = 2.00m i + 3.00m j – 6.00m k. Vector D = Å + B. Find the angle between vectors C and D.
Exercise 2. Directional derivative (6 pts + 9 pts) Let f(x,y,z) = xy + y2 – 23 – 105. 1) vf = a. yi + (x + 2y); – 3z2K b. (y + y2)i + (x + 2y); - 3z2k c. xi + (y + 2y); - 3z2K d. None of the above a. b. C. d. 2) The direction in which ſ decreases most rapidly at A(0,1,1) is: a. 14 14 c. wait tasta d tai-haiti e. None of...