Let F = xi + yj + zk, and let D be the cube bounded by the
planes x = y = z = +-1. Let S be the boundary of D. Verify the
divergence theorem...
1, and z 1. 3. Let F-zi +yj + zk, and let D be the cube bounded by the planes x-+1, y planes cl, Let S be the boundary of D. Verify the Divergence Theorem by showing JJJD
xi+ yj + zk 3. Given the vector field in space F(x, y, z) = or more conveniently, (.x2 + y2 + 22)3/2 1 Fr) where r = xi + yj + zk and r= ||1|| = x2 + y2 + x2 (instead of p) 73 r (a) [10 pts) Find the divergence of F, that is, V.F. (b) (10 pts] Directly evaluate the surface integral [/F F.Nds where S is the unit sphere 22 + y2 + z2 1...
(1point) Let r = xi + yj + zk and a = 4i +4j + 2k. (a) Find VG a). (b) Let C be a path from the origin to the point with position vector ro - ai+bj +ck. Find Jc VG a) df (c) If I I roll = 10, what is the maximum possible value of IV(F. , dF2 (Be sure you can explain why your answer is correct.) maximum value of Jc VG.ã di
(1point) Let r...
Please help me with Question B from the below question, and I
would appreciate if you include the steps. Thank you.
(2) Let r be the position vector zi + yj + zk, and let ρ be its length: (a) Calculate ▽2ρ2k, where k is a positive integer (b) Show that the vector field ρ_2r is conservative in the solid region {ρ > 0} (This region is Euclidean space R3 with the origin 0 removed.)
(2) Let r be the...
Consider the following vector field. F = (xi + yj + zk )/((x^2 + y^2 + z^2)^3/2) (a) Find the divergence of F. (b) Let S be any sphere not containing the origin. Find the outward flux of F across S. (c) Let Sa be the sphere of radius a centered at the origin. Find the outward flux of F across Sa.
9. Let Q be the solid bounded by the cylinder x2 + y2 = 1 and the planes z = 0 and z = 1 . Use the Divergence Theorem to calculate | | F . N dS where s is the surface of Q and F(x, y, z) = xi + yj + zk. (a) 67T (d) 0 (b) 1 (e) None of these (c) 3π
9. Let Q be the solid bounded by the cylinder x2 + y2...
Let F 9xi + yj + zk . S is the part of the surface z = -4x - 2y + 12 in the first octant oriented upward. ey 4,2,1 Find dA X * хр / Set up the iterated integral for flux 3 6 2x F.dA dy dx
Let F 9xi + yj + zk . S is the part of the surface z = -4x - 2y + 12 in the first octant oriented upward. ey 4,2,1 Find...
zi+yj + zk 3. Given the vector field in space F(x, y, z) or more conveniently, (x2 + y2 + 22)3/2 f where r = ci + yj + zk and r= |||| = V2 + y2 + z2 (instead of p) 1 F(r) = r2 (a) [10 pts] Find the divergence of F, that is, V.F. (b) (10 pts] Directly evaluate the surface integral lle F.NDS where S is the unit sphere x2 + y2 + z2 = 1...
can you solve this vector problems?
Find the outward flux of the vector field F(x, y, z) = (xi + yj
+ zk)/(x 2 + y 2 + z 2 ) 3/2 across the ellipsoid 4x^2 + 9y^2 + z^2
= 1.
6. (12 pts.) Find the outward flux of the vector field F(r,y, ) (ri yj+ zk)/(x2 + y2 22)3/2 across the ellipsoid 4r2 +9y2 + z2 = 1
6. (12 pts.) Find the outward flux of the vector...
1. The position of a particle is described as r=xi+yj, where i and j are the coordinate unit vectors in 2D Cartesian coordinates a?d x and y are the coordinates of a particle. The velocity can be calculated as v=dr/dt. Find an expression for v, by taking the derivative of r with respect to time. 2. a=2.00 t, where t is the time, in seconds, and a is the acceleration in meters per second squared. s=0 and v=0 at t=0....