(3) For the following velocity fields F on R3, find the flow along the given curve. r(t) = (t, t2, 1) F=(-4xy, 83, 2) with 0 2 t 1l F=(z-z, 0,2) r(t)-(cost, 0, sin t) with 0 t π F = (-y,2, 2) with r(...
Problem 4, Find, for 0-x-π, the arc-length of the segment of the curve R(t) = (2 cos t-cos 2t, 2 sin t-sin 2t) corresponding to 0< t < r
all questions clearly solved please (2) If the point of application of a force F: R3 R moves along a curve C, then the work done by the force is W F.dr. (a) Find the total work done on an object that traverses the curve c(t) (cos(t), 2 sin(t), (b) Find the total work done on an object that traverses the straight line from (1,0,-2) (c) Explain why the answers in the previous two questions coincide and provide a way...
Problem 7. Given that each of the following vector fields F is conservative Find a potential function f such that f = F and evaluate fe F dr along the given curve C 1. F(r,y) y C: F(t)(t3- 2t, t3 + 2t), 0 <t<1 2. F(x,y, ) yze"* i + e#* j + xye k C: F(t)(t2 1)i +(2 -1)( -2t)k, 0t 2
2. Compute | F. ds for each of the vector fields F and paths r given below: (b) Ple:) - (a ) and re) – () witte (0.1 Fler,1,2) = ( and r(t) = ( ) with t e (0, 2). F(x, y, z) = | 22 and r(t) = with t€ (0,2). F(x, y, z) = sin Cos y 32 and r(t) = -t with t € (0,1). (a) F(x, y, z) = | Vies:)-( .) --( * )-464...
3. 8p] Show that the force field F(x,y, z) sin y, x cos y + cos z, -y sin z) is conservative and use this fact to evaluate the work done by F in moving a particle with unit mass along the curve C with parametrization r(t (sin t, t, 2t), 0 <t<T/2. 4. 8p] A thin wire has the shape of a helix x = sin t, 0 < t < 27r. If the t, y = cos t,...
Please help solve the following question with steps. Thank you! 3. Suppose that an object moves along the helix r(t) - (2 cos t, 2 sin t, L.) , 2π subject to the force field F-(-y, x, z). Determine the work 0-t done. 3. Suppose that an object moves along the helix r(t) - (2 cos t, 2 sin t, L.) , 2π subject to the force field F-(-y, x, z). Determine the work 0-t done.
If C is the curve given by r (t) = (1 + 4 sin t)i + (1+2 sin2t)j + (1 + 3 sin3t) k, 0≤t≤π/2 and F is the radial vector field F(x, y, z) = xi + yj + zk, compute the work done by F on a particle moving along C.
If C is the curve given by r(t) = (1 + 3 sin t)i + (1+2 sin2t) j + (1 + 5 sin3t) k, 0 ≤t≤π/2 and F is the radial vector field F(x, y, z) = xi + yj + zk, compute the work done by F on a particle moving along C.
F- [y - yz sin x,x + z cos x,y cos x] from OstsT/2 where the path is defined as follows x- 2t y = (1 + cost)2 z- 4(sint)3 m. F= [8xy®z, 12x2y®z, 4x2yaj from (2,0,0) to (0,2,π/2). The path is a helix of radius 2 advancing 1 unit along the positive z axis in one period of 2Tt. We were unable to transcribe this image F- [y - yz sin x,x + z cos x,y cos x] from...
for the curve r(t) find an equation for the indicated plane at the given value of t 56) r(t) (t2-6)i+ (2t-3)j+9k; osculating plane at t=6 A) x+ y+(z+9)=0 C)x+y+ (z-9)-0 56) B) z-9 D) z -9 (3t sint+3 cos t)i + (3t cos t-3 sin t)j+ 4k; normal plane at t 1.5r.. A) y=-3 57) r(t) 57) B) y 3 C)x-y+z-3 D) x+y+z=-3 56) r(t) (t2-6)i+ (2t-3)j+9k; osculating plane at t=6 A) x+ y+(z+9)=0 C)x+y+ (z-9)-0 56) B) z-9 D)...