Question 9 Using Lagrange multipliers, find the point on the plane x + 3y + 72 = 1 that is closest to the origin. Enter the exact answers as improper fractions, if necessary. (x, y,z) = Edit ? Edit ? Edit
TOTAL MARKS: 25 QUESTION 4 (a) Find a normal vector and an equation for the tangent plane to the surface at the point P: (-2,1,3). Determine the equation of the line formed by the intersection of this plane with the plane z = 0. 10 marks (b) Find the directional derivative of the function F(r, y, z)at the point P: (1,-1,-2) in the direction of the vector Give a brief interpretation of what your result means. 2y -3 [9 marks]...
7. [2 marks] Find a unit vector normal to the plane with equation x + 3y-4z = 5.
Question 8 Find an equation for the tangent plane and parametric equations for the normal line to the surface at the point P. sin 20 Tangent Plane: z= ? Edit Normal Line: x(t) = ? Edit ) = Edit z(t) = 1 - 1 MapleNet
Question 8 Find an equation for the tangent plane and parametric equations for the normal line to the surface at the point P. Р 14 Tangent Plane: z= Edit Normal Line: X(t) = ? Edit y(t) = Edit z(t) = 1-t
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)
Question 8 Find an equation for the tangent plane and parametric equations for the normal line to the surface at the point P. Z= =e&y sin 8x: P 16 P G6,0,1) Tangent Plane: z = ? Edit Normal Line: X(t) = 2 Edit yt) = Edit z(1) = 1-1
Question 9 Let r(t)={cos 2t, sin 2t, V5t) a) Find the unit tangent vector and the unit normal vector of r(t) at += TI (Round to 2 decimal places) TE)= NG) = < b) Find the binormal vector of r(t) at t = TT 2 (Round to 2 decimal places) BC) =< A Moving to another question will save this response.
Question (1a): Find gradient of g at P. Question (1b): Find a unit vector that is normal to the surface g=5 at P. Question (1c): Find the deriative of g at P in a direction parallel to the line whose parametric equation is shown Question 2: Verify the forcefield is conservative. Find the potential energy U for which F=-(gradient)U Please Show all work. Thank you 1. Consider the function g (r,y,z) 2 -y and the point P (8,4,1) (a) Find...
Find the Unit Normal Vector and Unit Binormal Vector: ( 1 point) Consider the helix r(t) (cos(8t), sin(8t),-3t). Compute, at- A, The unit tangent vector T-〈10.8 10884854070| , -0.46816458878| B. The unit normal vector N 〈 C. The unit binormal vector B-〈 1 ǐ ,1-0.35 11 23441 58 0