14. A vector that is normal to the graph of z=x² + y2 +7 at the point (2,1,12) is a) 4ỉ +29 – Ã b) î–2j+3ỉ c) 7î++4k d) – 6 –2j + k e) none of these
Question 19 Find a normal vector of the tangent plane to 2? + y2 + x2 = 30 at the point (1, -2,5). (1,2,5) O (2,-4,-8) (-3,6,-12) None of the above or below (-2,4-10) (1,1,1)
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.
Directions: In 7-10, determine the rectangular equation given its polar form. [7] = 9 A. x + y2 = 3 B. x + y2 = 9 C. x² + y2 = 81 D. x + y = 9 [8] r = - 179csce A. X = -179 B. x = 179 c. y = -179 D. y = 179 E. none of these [9] @ = 13 A. y =- 13 3 x B.y = c. y = -13 D....
Let S be the sphere r2 + y2 + z2-k2 oriented outward and let F be the vector field (r, y, 2)/(a2 +y2 +2/2. Find (i) the normal vector field n on S (ii) the normal component of F on S and (ii) the flux of F across S Let S be the sphere r2 + y2 + z2-k2 oriented outward and let F be the vector field (r, y, 2)/(a2 +y2 +2/2. Find (i) the normal vector field n...
Find the slope of the normal to the graph of x^2-7xy= 7+2y^2 at the point (1,2). I will thumbs up!
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...
The equation of the plane which is normal to the vector m=< -5, 11,8 > and contains the point P(4, 2, -1) is: a. 5x-1 ly-8z=6 b. -5x+11y+87=5 C. 4x+2y-z=-6 d. None of the above. The exact value of the position vector - [] that is formed when the initial position vector 01 = 4] is first rotated 45° in an anti-clockwise direction and then stretched by a factor of 3 is: a. Sale Sale b. = C. 61 =...
1. Given that u = 101 - 59 + 3k and 7 = -4î +29 - k, compute each of the following. (a) 5ū + 2v (b) ||5u + 20 || (c) ü. (d) ūxy (e) the angle between ū and (f) the projection of u along v