Example 1. The primitive translation vectors of the hexagonal space lallice may De taken as -> a = (V3a/ 2)î + (a/ 2)j; b = -(J3a/2)î + (a/ 2)j; c = ck (aj Show that the volume of the primitive cell is (V3/2) a² c (b) Show that the primitive translations of the reciprocal lattice are 4 = (2m//3ajî + (2n/ a)j; B = - (2r//3kajik(2n/aj;C=(2T/c)k

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A: Let  be a linear transformation from  to  with associated matrix .Let  be a linear transformation…

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A: The given problem is to find the distance between the given two planes. Given planes 2x+3y+4z=4 and…

Q: 1. Get center point of homo geneu us plane limited by 9) y =4- x2 and x axis

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer one question at a…

Q: 21) Find the area of a triangle fosmed from the twovectors a = L'+2j-k-.

A: Given, a ⇀=i+2j-kb⇀ =2i-j+4k

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A: A branch point of an analytic function is a point in the complex plane whose complex argument can be…

Q: Show that the following gn are harmonic and find its conjugate u=3x^2y+2x^2_y^3_2y^2

A:

Q: Triangle XYZ is drawn with vertices X(1, 2), Y(2, 5), Z(3, 4). Determine the translation direction…

A: Vertices of a triangle XYZ: X=1, 2Y=2, 5Z=3, 4

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A: Solving two equations

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A:

Q: Find the shortest distance from (1,1) to (1,2) on hyperbolic plane.

A: Here we take the  (1,1) to (1,2) on hyperbolic plane.    for example we take this    d(x,y) = a cosh…

Q: (5). If A, B and A+B are each non-singular and the products are conformable, prove that (a). A(A +…

A:

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A:

Q: Let flox) - I=39 1-3x %3D

A: Answer and explanation is given below

Q: -}]-=[}]»=[}- [] 3 Find Let vị = and p = 3 a hyperplane [f: d] (in this case, a line) that strictly…

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Q: 1. Find a parametrization of the line segment L from -2 to -2 + 2i. 2. Find the image of L under the…

A: We will find the equation for L and the image of L under w

Q: Explain the conditions for the origin a node of the system x' = Ax?

A: The system of the first order differential equations x'=Ax is homogeneous and the matrix A is an n×n…

Q: Derive a cubic spline with natural boundary condition using the following points: (−2, 1), (0,0),…

A: Sol:-] To derive a cubic spline with natural boundary condition, we need to find the cubic…

Q: 17. [Shadows] Consider the parallelogram surface whose vertices are (0, 0, 1), (2,0, 1), (3, 2, 1),…

A:

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A: A rotational matrix, also known as a rotation matrix, is a special type of square matrix used to…

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Q: Suppose the solution set of x1 + x2+2x4 What are the equations of the plane at (1,2,3,4) which is…

A: First we find direction vectors of the plane of solutions.

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Q: What is the distance between the point (4,-&, 1) and the plane 5x-z= 2y+5?

A: