5. Let A be an antisymmetric Cartesian tensor with components A¡j. Show that for any Cartesian vector b with components b; one has b · Ab = A¡jb;b; = 0.

Q: 4. Let A and B be n x n matrices with AB = BA, and let |v) E C" be an eigenvector of A with…

A: Given:-            Bxi = ∑i=1r  cij xi                       i = 1,2,3,......r

Q: 22 a Consider a system with j =1. Explicitly write (j=1, m|J,\j=1, m) in 3x3 matrix form.

A: The raising and lowering operators for angular momentum are such that

Q: the 8 ball into the top right corner pocket to win the game, but you want to make sure that you…

A: Solution:   From the above-given data,   Mass (m)=0.15 kg Time(∆t)=0.1 s   Let us draw a figure to…

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: 8. Find the vector product of two vectors A| = 50 and B| = 20, with an angle %3D between them is…

A: Vector product is defined as- A*B = |A| |B|sin(theta) A*B = 50*20*sin(45)

Q: for the J component your answer could be simplified to L/pi correct?

A: the answer provided in the existing answer of this question is the j component of the answer…

Q: 4 i + V41 Suppose i -k and u = 2i + 5j. Compute the following: %3D %3D V41 lū| = %3D ... II

A: Given: v→=441i+541ju→=2i+5j

Q: A four vector [A] and a tensor [B] are defined by: [A] = (-2, 7, 1,3) 1 3 -5 7 0 2 0 -1 5 5 2 6 -3…

A: given information=(-2 ,7, 1 3)

Q: In cylindrical coordinates, a vector function of position is given by f = r² zer +4r²e + 2zęz…

A:

Q: Given the function D= 3x²y - y³z², find the gradient VQ. b. a. 6xyî+ (3x² - 3y²z²)ĵ- 2y³zk…

A: Given, Φ = 3x2y - y3z2

Q: The surface integral of V = x + yŷ + (z - 3)2 over the sphere of unit radius centred at the origin…

A: The objective of the question is to calculate the surface integral of the given vector field V = x +…

Q: P.1: Let lu) = (). In) = (). a) Find the norm of Ju) and |v). Are these vectors normalized? b) If a…

A: We have to perform the following operations mentioned above regarding the ket vectors mentioned…

Q: Let A=5i-6.5 and B=3.5i-7ĵ . If lies in the xy-plane, Cis perpendicular to À , and Č-B=15 , what is…

A:

Q: Given the function y =3xyz2î + 2xy³j-x2yzk Find the curl Vxu a. 3yz'i + 6xy2j - x²yk b. Зyz? + 6ху?-…

A:

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: Evaluate [[ F · ndS (i.e., find the flux of F across S) where F(x, y, z)=-y, x, z² > and S is the…

A: Given F→ = -yx^ + xy^ + z2k^ x2 + y2 + z2 = 4 as the hemisphere is oriented in the direction of the…

Q: Let /be the line through the point with coordinates (0,1,0) in the direction of the vector 1 0 their…

A: Given, l be the line through the point with coordinates (0,1,0) in the direction of the vector…

Q: b) Write down the two components of the geodesic equation.

A: The objective of the question is to derive the components of the geodesic equation for a sphere of…

Q: Use Stokes' theorem to evaluate SF. dr where F = z²î + y²ĵ + xk and C is the triangle with vertices…

A: