In a simple orthorhombic system two lattice points are connected through the translation vector T=2a+3b+4c,  where a=2Å, b=3Å and c=4Å. Determine the direction of the translation vector.

Q: The positions vectors R1and R2 of the two atoms 1 and 2 in a crystal have equal magnitudes. If the…

A: The answer is c.

Q: A rigid body that can rotate and translate over a plane (e.g., a car) has a three dimensional…

A: Concept used: Transformations for a system are represented by rotations and translations.

Q: Q3: A: Determine the Miller Indices and planes of the following: 1/2 2/a 1/3 1/2

A: This question can easily be solved by applying the basic concept of Miller Indices

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: Consider a rectangular surface of length L and width W in the xy plane with its center at the…

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Q: Use qualitative arguments (i.e., draw surfaces and/or loops on the plots and ascribe mcaning to the…

A: Loop drawn in the diagram shows that vector field has non zero divergence since net arrows are…

Q: Evaluate the Clebsch Gordan coefficients for 3 J₁ = ³/2, J2 = 2/1/2

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Q: Use the law of sines and the law of cosines, in conjunction with sketches of the force polygons, to…

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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: Find a unit vector normal to the surface xy? + xz = 1 at the point (–1, 1, 1).

A: Given surface-xy2+xz=1P=(-,1,1)

Q: Determine the magnitude of the following cross product: ( 11 7 +57 ) X (27 +57)

A: Given: The vectors are 11i+5j and 2i+5j

Q: y extend this idea to cylindrical o, z), which you may think of ar coordinate system with the cked…

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Q: sin dz. (b) sin° z dz. (z - T/6) Given C is the circle |z| = 1. Find the value of (a) z- 7/6

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Q: A (-3; 2; 0), B (0; 0; 6), C (2; -3; 0) and D (0; -3; 0), Since FBA = 152, FBC = 201 and FBD = 192,…

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

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Q: Consider the vectors A = (-8.1,5.4) and B = (10.7,-9.1), such that A - B +2.7C = 0. %3D

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Q: Let 2 vectors å anb b a 121=53161-5 in the plane of modules. How much is the magnitude of their e…

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Q: If A = 2yz i – (x +3y – 2)j+ (x² + z)k, evaluate SS, (V × A)· dS over the surface of intersection of…

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Q: Graphite is lamellar crystal in which single layers of carbon atoms or graphene are distributed at…

A: Graphite is lamellar crystal in which single layer of carbon atoms. Graphene has hexagonal, 2-d…

Q: Q 2: Prove that in the hexagonal structure the vectors of the inverted lattice are given. According…

A: α*=α=90° β*=β=90° γ*=180-γ   Draw the figure as below.

Q: (3) (5 pts) Consider two vectors A, B which has the following forms: A = A,i + A,3 + A¸k, B = B,ì +…

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Q: Problem-3: For Vector function, A = (x + yz)i + 3(2xz +y²)j — (xy)k (a) Verify the Divergence…

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Q: Calculate the commutators [^px2, f(^x

A: Find commutator of px with x^2

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: two complex numbers z1 = 7.9 + i 21.1 and 22 = 14.4 - i 32.2 Find the the magnitude of the z where…

A: Given : z1=7.9+21.1iz2=14.4-32.2i

Q: In a given situation, the orbit of the particle r=3a/(4-cos(3theta)). Using expression dr/d(theta)…

A: Given the equation of central orbit r=3a/(4-cos(3theta)).  Then we can find the apsidal angel as…

Q: Solve with explanation and calculation

A: By multiplying normal vector by -1 doesn't change anything for the plane.you can also reduce the…

Q: Distinguish between space lattice vectors (a1, a2, a3) and reciprocal vectors (b1, b2, b3)

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Q: Find the centroid of the solid bounded above by the paraboloid z = x? + y?, below by the plane z = 0…

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Q: Express z =2+√2i in polar form.

A: Concept used: Polar form is expressed using r,θ co-ordinates.

Q: 1 Consider the plane passing through the three points O, A, B, given by Oi + 0j + Ok A = i+2j + 3k…

A: First, we find two vectors that are in the plane using the coordinates of the points given. Then, we…

Q: Anil

A: The objective of the question is to find the tt component of the energy-momentum tensor T_ab for the…

Q: For the inner product (|4) the left side o always be the conjugate value O True O False

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Q: Coordinates of the points are given as: A(x, y, z) = A(-2,3,8) B(x, y, z)= B(5,3, 8) C(x, y, z) =…

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Q: z-3 Evaluate $c 2?+2z+5 1 and C : |z+1 – i| = 2. dz = "(i – 2). dz where C : Ans. fo z dz = 0 and fo…

A: Given, ∮ C z-3z2+2z+5dz

Q: show a specific vector (eigenvector) of the y-axis spin matrix. ħ 0 Sy ( (13) == 2 i

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Q: A crystalline solid consists of atoms stacked up in a repeating lattice structure. Consider a…

A: Given  Distance between atoms, L = 0.200 nm

Q: 3 - Given a scalar field T = (x +3)y² sin(2z) and a vector field Ä = ryi + y²(z+5)k, calculate (3)…

A: The gradient function is given by: ∇⇀=i^∂∂x+j^∂∂y+k^∂∂z Thus, we will use this expression to solve…

Q: What are the angles between angular momentum vector L→ and positive z-axis for each allowed value of…

A: please see the next step for solution