The transformation relating Cartesian and cylindrical coordinate is p = (x² + y²)¿ 0 = tan¬ x = p cos 0, y = p sin 0, z = z, Show that the gradient operator in cylindrical coordinates is given by z = Z 1 V= pa, + ÷@aq + 20z

Q: Which of the following matrices are hermitian? Choose all that apply.

A: We need to select which matrices are hermitian from the given matrices.

Q: d) Having seen how the inner product behaves under rotation we can now investigate its behaviour…

A: Given that a vectorvi​transforms under the Euclidean group as: vi​→Oij​vj​+ai​(4)where the…

Q: Evaluate the commutator [d/dx,x2], considering:     (a) an arbitrary function f(x).     b) f(x)=x3-3

A: To find :  To solve the Commutation bracket.  Formula used :  Commutation of [ A, B ] = AB - BA

Q: Consider a vector field F = 2 pzap+3z sinyap- 4P cosp az. Evaluate the circulation of Fover the path…

A:

Q: For the scalar potential field f = x^2*y^3 + x*y^2*z^3 + c, what is the direction and magnitude of…

A:

Q: Consider the following kets: 2 i |r,) = +|1+ i y Ir2) = [-3i . 2- 2i 4 (ri \r2) and a) compute the…

A:

Q: A triangle in the xy plane is defined with = (0,0), (0, 2) and corners at (x,y) (4, 2). We want to…

A: The triangle has corners at (x,y)=(0,0), (0,2) and (4,2). We have a function f(x,y) which we need to…

Q: If A = 2i − j − k, B = 2i − 3j + k, C = j + k, find (A · B)C, A(B · C), (A × B) · C,A · (B × C), (A…

A: (A•B)C = (2i − j − k • 2i − 3j + k)( j + k) (A•B)C = (4 + 3 - 1)( j + k) (A•B)C = 6( j + k)

Q: In the Eigen vector equation AX = XX, the op 32 ¹ = [³2] 41 Find: A (a) The Eigen values > (b) The…

A:

Q: Determine the following indefinite integral up to a constant c: ∫(sin(3?+7)+cos(7?+3))?? Select…

A:

Q: Prove that the vector V(x, y,z)= 3y*z°i+ 4x'z*j+3x*y°(-k) is solenoidal. 4.1 k 4.2 Show that the…

A: A vector is solenoidal if its divergence is zero. A vector is irrotational if its curl is zero.

Q: If  and B are two vectors that commute with Ô, prove the useful identity (Ô· Â)(Ô · B) = · B+ iÔ(Â…

A:

Q: Find the unit vector ev if vector v = <3,2>

A:

Q: Prove that the vector field F(x,y,z) = (x^2 + yz)i − 2y(x + z)j + (xy + z^2)k is incompressible, and…

A: We have been given a vector field and we need to show that its incompressible and also need to find…

Q: Evaluate both sides of the Divergence Theorem of the given vector field D = ye* ax + z(xy)? ay + (x…

A:

Q: x=J_y=K Z=L Let Ġ(J, K, L) = for c, d E R. Find c and d that will make the curl of G (1, zero, 2)…

A: Given, G→x,y,z=<3cx2z,ey+d+xz,xyz>

Q: Given the vector field v = (xy²)t + Gy³z²)j – (x³yz)k determine if it is converging, diverging or…

A:

Q: A→ times B→ = What is the angle between A and B? What is 2B times 3C?

A: Expanding this determinant:A×B =i[(1)(1)−(0)(−4)]−j[(2)(1)−(−4)(−3)]+k[(2)(0)−(1)(−3)]…

Q: Suppose that A,, is a covector field, and consider the object Fμv=O₁ Av - O₂ A₁. (a) Show explicitly…

A: The objective of the question is to prove that the definition F = ∇A - ∇A, which uses the covariant…

Q: In a vector field V = (x^a, y^b, z^c) what is the value of ∇.V at (x, y, z) = (d, e, f) with a = 3,…

A: The divergence is given by,  div=ddxx^+ddyy^+ddzz^Given vector field V is, V=xx^+yy^+zz^

Q: The component form of vector is 7 = (4, 3). v Find 47. 40 =

A: A vector can be represented by its component form. The vector has two components in a…

Q: gradient vector field Vf

A:

Q: Find the angle that is complementary to u.

A: Given, Angles to find out their Complementary angles

Q: A type (0,4) tensor Tabcd satisfies TabedAºµ°X°µd = 0 for all con- travariant vectors X and uº. Show…

A:

Q: Suppose that you have two vectors (1,0,0, 1) (2,0,0, 2) at What is a"b,?

A: Given that aμ=(1,0,0,1) and bμ=(2,0,0,2) we have to find the value of aμbμ

Q: the eigenvalues of the following matrix: /2 2 0 220 0 0 A) 0, 1,4 B) 1.2.2 C) 5,0,0 D) 5, 5,0 E) 0,…

A:

Q: An Operator O  is said to be linear if O{c1 f1(x)+ c2 f2(x)} =c1 O f1(x) +c2 O f2(x). Check the…

A:

Q: Find a scalar potential, fi, if  F=(3x^2yz^2)i+(x^3z^2)j+(2x^3yz)k, and fi(1,1,1)=1

A:

Q: Given F(x, y, z) = (x³ + cosh z) i + (2y³ – 3x²y)j – (x² + 4y²z) k. Use Gauss's theorem to calculate…

A: Given that:F→=(x3+coshz)i^+(2y3-3x2y)j^-(x2+4y2z)k^Surface bounded, x=0, z=0x+z=6x=4-y2To…

Q: Calculate the first derivative of the function f(x) = 2x e -X at the point x=1.19. Express the…

A:

Q: P13.25 Make the three polynomial functions ao, a₁ + b₁x, and a₂ + b₂x + c₂x² orthonormal in the…

A:

Q: Calculate the commutator 2m between the kinetic energy and the position operators for a particle…

A:

Q: iven l, find the form of the potential U(r) such that the path of a particle subjected to this…

A: The differential equation of the orbit is given as  d2udϕ2+u=-mL2u2f1u…