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: Problem 7: Two vectors in Cartesian coordinates have components A = (3, 2, 3) and B = (4, -1, 7).…

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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: A = (2, -4) and B = (-3,3). Determine the distance between points A and B and find their polar…

A: Two points given in the xy plane  A = (2, -4) and B = (-3,3)   Find: Distance between the A and B…

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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: Vectors A→A→ and B→B→ both have a magnitude of 8. If their resultant has a magnitude of 10, what is…

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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: Consider the solid D given by {(r, y, 2) € R°; ² +y° <z<2- V + y?}. D = Let F(x, y, z) = (2rz + e)i+…

A: The Divergence Theorem or Gauss's Divergence Theorem was invented and proved for the first time by…

Q: Show a[1 2 1] direction on a simple cubic unit cell and give the location (in correct notation) for…

A: The required direction vector for [1 2 1] is shown in the figure below.

Q: Given a vector (77, 48, 22) and another vector (4, 49, 67) what is the z-component of their sum?

A: Given that Vector 1 (A)= (77, 48, 22)  And , vector 2 (B)= (4, 49, 67) Let i, j and k be the unit…

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: For a colloidal sphere moving under the influence of Brownian motion in3D, what is the value of ,…

A: The average velocity of the colloidal sphere moving under the influence of Brownian motion in 3D is…

Q: Find the x− and y− components of the vectors A~, B~ , C~ , and D~ . Take A = 10.0, B = 7.00, C =…

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Q: Compute the flux of = a bounded below by the plane from the z-axis. + y + zk through the curved…

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

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Q: The angle between the vectors that connect ther carbon atom to the hydrogen atoms in the methane…

A: Introduction: A bond angle is an angle formed between three atoms across at least two bonds. For…

Q: Let R be a region in 3-space having volume 5, centroid at (x. y, 2) (-1,2, -3), and a piecewise…

A: Concept used: Divergence theorem is used. It relates flux through a vector field to its divergence…

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: The displacement distance of an atom around a dislocation (line defect in a crystal or grains) is…

A: From the definition of the edge location, it is known that the Burgers vector is always…

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: Problem 2 Identify the Miller indices for the direction shown in (a) and the plane shown in (b).…

A: a The Miller indices for the direction shown is obtained by: x y z=34 12 ∞ Take a reciprocal to get…

Q: Find the point at which the line meets the plane. x = 1+ 6t, y = - 2+ 2t, z= - 2+ 5t; x+ y+z= - 3…

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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: 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: Four vectors:  a´ = [1 2 3], b´ = [1 0 -1], c´ = [1 2 3 4], d´ = [2 1]. Compute each of the…

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Q: Steiner’s theorem and gyration radius. A metal tank wheel in the shape of a disc of radius R is…

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

A: Let F1, F2, and F­3 denote the three forces, θ1, θ2, and θ3 denote the three angles of the forces…

Q: If R= Z16, give me the graph of Z16 on singular ideal Z(R),( since a & b are adjacent if ab belong…

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Q: Consider the 3D vectors C and D defined as C = 4i + 5j - 12k and D = 12i - 8j + 2k. Which of the…

A: Given,  C = 4i + 5j - 12k   And  D = 12i - 8j + 2k

Q: Problem 2 (Nodal Analysis): Find V. Express the result in polar form. j4 Q + Vx 2/0° A 5Ω -j3 2 (4)…

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

A: Given: The resultant magnitude R and the angle θ between the x-axis and the line of action of the…

Q: Two vectors in Cartisian coordinates have components A= (2,2,3) and B =(4,-1,7). What is the dot…

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Q: Vector A has a magnitude of 4 m and lies in the xy plane directed at 45 degrees counterclockwise…

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Q: The resultant of two vectors is 20 units long and makes angles of 20o and 50o with the two vectors,…

A: Given, Length of resultant,R=20 units Angle of resultant with vectors,θ1=20°,θ2=50°

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

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