Q3:A force described by -xx zz yŷ 2 x+y2+: + 2 x²+y 2+y 2 2 2+z 1- Express F in circular cylindrical coordinates. 2- Calculate the curl of F F is conservative or not. 3- Calculate the divergence of F .

Q: If a and b are integers, then a/b is always a rational number. True False

A:

Q: Sketch the graph of the parametric equations x = sint, y = 2 cos(3t), π ≤ t ≤ 27. Clearly label the…

A: We are to sketch the graph of the parametric equationsx = sint, y = 2 cos(3t), π < t < 2π.…

Q: Let fery) Ts TS a diff eran tiable function. eron The directional Jeri ve dive of fuiyl in the direc…

A:

Q: Express the vector field B = (x^2- y^2)ay + xzaz in spherical coordinates at ( 4, 30o, 120o) *…

A: Relation between cartesian and spherical co ordinate system x= r sinθ cosϕ   , y = r sinθ sinϕ   ,…

Q: Find the directional derative of f at the point P0(1,1) in the direction of the vector A = 3i - 2j…

A: Direction derivatives at (1,1) is given in direction of A = 3i - 2j.

Q: A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector…

A: Given that v=<x-y, z+y+9, z2> and the given curve is y=1-x2-z2,y≥0 To find: The value of ∬S…

Q: QI-A) Fnd the position, vekocity and the speed of the vector function ( r(t) ) that given bekow at…

A: Given vector function is r(t)→=t2i-t3j To find the position, velocity and the speed of the vector…

Q: -y+25 Let F (x, y, z) := x+yz7 3+2⁹ let n be the outward unit normal vector. Evaluate Sf (curl F) ·…

A:

Q: A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector…

A: Adding the plane surface y=0 to close the surface and apply the gauss divergence theorem.

Q: Sketch and describe the vector field F (x, y) = (-y,2x)

A: The given vector field is F→x,y=-y,2x A vector field F→ in ℝ2 or ℝ3 is an assignment of a…

Q: Find r'(t), r(t), and r'(t) for the given value of to. Then sketch the space curve represented by…

A:

Q: Evaluate :// F. d5 , where F = and S is the helicoid with vector equation r(u, v) upward…

A:

Q: 4. Consider the vector function r(z, y) = (x, y, x² + 2y*). (a) Re-write this vector function as…

A: For the given vector function, PART A The surface function is given by, f(x,y)=xi^+yj^+(x2+2y2)k^…

Q: Evaluate 1+ x° + y°dS, where S is the helicoid with vector equation т(и, и) — 0 <u < 3, 0 < v< T

A:

Q: Q1] Find a unit vector normal to the surface 3x2 у — узz? аt the point (1,-2, -1)

A:

Q: 7. For the vector-valued function √t-1 ln(2t - 1) t² - 1 r(t) = (VI- t-1 2 COS πt rt), (t (t = 1):…

A: Let us solve above problem

Q: Calculate vector field F = (2-z²+2-x²)i + (2 · y³ + 4·x)j + (2x²z³+2)k a flux from a box with the…

A:

Q: A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector…

A:

Q: The force exerted by an electric charge at the origin on a charged particle at the point (x,y,z)…

A:

Q: A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector…

A: Given data net velocity (v) V=x-y, z+y+9, z2 net equation  y=1-x2-z2   , y≥0 find  ∫∫sv.ds= ? in…

Q: The position of a particle is determined by the vector-valued function r(t) = (1 - 12,3t, 1³). Find…

A:

Q: For the scalar function f, div(grad f) is equal to Select one: a. + + dx?' ay? ' az? b. dx dy dz C.…

A:

Q: ed by F(x, y) = (-: %3D

A: The function given is , F→x,y=-x,y. Draw the table for the points plot on the graph for the vector…

Q: Let C be the straight line segment in the xy-plane from the point (1, 2) to the point (5, 3). Let F…

A:

Q: 2. Let x'= [5, 1, 3] and y' =[-1, 3, 1]. (a) Find the inner product, y'x. (b) Find x- - 2y. (c) Find…

A:

Q: Let f,g be scalar functions, ủ be a vector function, and assuming sufficient differentiability. Then…

A: