8. A plate is bounded by the positive x and y axes and the curve y=3-Vx . Find the second moment of area of the plate with respect to the x-axis.

Q: 1. Show that the following vector field is conservative: F = (4 xy - 2z)î +(2 xr² - 6 yz ) j +(-3 y²…

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Q: Q1. Force F = {270i + 450j –140k} N and it passes point B. The coordinates of the points are: A (21,…

A: GivenF→=270i+450j-140kNow AB→=OB→-OA→AB→=0,0,21-21,0,0AB→=-21i+0j+21kNow the moment at A is given…

Q: 1. Show that the following vector field is conservative: F (4 xy - 2z)î +(2 x² - 6 yz ) ĵ +(-3 y² -…

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Q: 1 ) T = cos 0 a, + r sin 0 cos o a, + cos 0 aó .2

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Q: 1. Find the curl of the following vector fields a) V= = (3xz², -yz, x + 2z)

A: Given V=(3xz2,  -yz,  x+2z)

Q: Find the resultant force and the angles the resultant force makes with all three axes. Assume values…

A: Consider the values of x=7 m and y=8 m.

Q: the vectar sumÃtB the vector difference AB and B-A

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Q: For vectors A = - 10i + 5j + 12k and B direction of B Submit Question – 3i – 7j + 7k, find the…

A: Given data: A→=-10i+5j+12kB→=-3i-7j+7k Need to determine the projection of A→ along the direction of…

Q: Use a triple integral to find the volume of the given solid. The solid enclosed by the cylinder x2 +…

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Q: Calculate the Inner (dot) product between pair of vectors given below. Calculate the angle between…

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Q: The moment of the force F=180-lb about the point O in Cartesian vector form is. B 4 ft 2 ft 4 ft

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Q: What is the y-component and magnitude of A?

A: The problem is asking for the y-component and the magnitude of a vector A. We know that the vector…

The Space Lattice and Unit Cells

Every matter consists of atoms, molecules, and ions. If these atoms, molecules, and ions (micro-particles) are represented in a three-dimensional space-occupying certain specific points in space, then these arrangements are termed as space lattices and the specific points which are being occupied by atoms, molecules and ions are termed as lattice points. The atoms, molecules, and ions at the lattice points are generally grouped in a regular fashion and repeat periodically at the three-dimensional space.