If the vector A(x,y,z) is perpendicular to the closed surface S prove that: where T is the volume enclosed by the

Q: For each of the following vector fields F, decide whether it is conservative or not by computing the…

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Q: Find the Miller Indices of a plane whose intercepts are (2,1,3).

A: Given intercepts are (p,q,r)= (2,1,3) The Miller indices of a plane is    h,k,l=1p,1q,1r…

Q: Evaluate the given integral. Jx²Inxdx

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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: Find the following vector product B x B.

A: From the given diagram: The x-component (horizontal component) of B→ is       Bx = Bcos53o =…

Q: Show that if a matrix is orthogonal and its determinant is +1, then each element of the matrix is…

A: Let A is an orthogonal matrix with determinant equal to+1. Orthogonal matrix, AAT=1…

Q: Consider the following Hermitian matrix 3 1 i 2 1i a) find the eigenvalues find the eigenvectors b)…

A: (a)The eigen values is,

Q: Prove that

A: To prove: It is known that:

Q: Given the following matrix 3 3 1 5 Find its two eigenvectors. (A 3 and H2 0. B 3 and A, !! R -3 and…

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Q: Find the following vector product A´x (F +2C ).

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Q: Determine the projection of force F = 80 N along line BC. Express the result as a Cartesian vector.

A: Given, F = 80 N We need to find the projection of F along BC and express it in a Cartesian vector.

Q: A docs.google.com/forms/d/e Which function is preferable to find the magnitude of a complex number?…

A: 1. Correct option is : abs ()

Q: Evaluate the surface integral /| (2xzdydz + ydzdx + z?dxdy) where S is a closed surface, given by S:…

A: Given:I = ∯S 2 xz dy dz + y x dx dz+…

Q: (Vector analysis) Given the function v with cubic volume having sides of length 2 from the origin as…

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Q: Let P:(-1,2,3), Pa(2,-1,1) and Pa(1,1,1) area of the triangle equal..

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Q: a- Construct the 2-dimensional matrix A that representing the effect of operator  on the…

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Q: If f is a scalar function and v = [v1, v2, v3] is a vector field. Show that div(fv)=f divv+v·∇f

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Q: du (a) Let u be a differentiable vector function of constant length, then show that u. = 0. dt

A: Note: As per Bartleyby's guideline one question has to be solved at a time. So, upload other…

Q: Derive a formula for the centroid of section U in the figure below, in terms of r and h and in…

A: The centroid is a centre point of an object. In other words, if we have to replace the object with…

Q: Let a = and b = . %3D (a) Find the scalar projection of b onto a. (b) Find the vector projection of…

A: A=(-2,2,1)  ,  B=(-5,-4,3)then,a→=-2L^+2j^+k^…

Q: Consider a vector field of A = (2x-z) i + xyj - x ²k taken over the region (a cube) bounded be x =…

A: Vectors are physical quantities that have both magnitude and direction. Scalars on the other hand…

Q: Given vectors: A(7,4,2), B(0,3,5) and C(8,2,2) forms a triangle. Find the unit vector in the plane…

A: A(7,4,2),B(0,3,5),C(8,2,2) forms a triangle.

Q: Set up the triple integral of an arbitrary continuous function f(x, y, z) in spherical coordinates…

A: Please see the answer below

Q: *Problem 3.17 The 2 x 2 matrix representing a rotation of the xy-plane is cos 0 - sin 0 cos e T =…

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Q: Get the expression for the divergent of a vector field in spherical coordinates.

A: Given : Divergence :                           Divergence of a vector field is a measure of the “…

Q: Find the simplest SI unit of z, if Z = Fr³r? m³v²

A: Write the given values of this problem.  Let, F=force (kg.m/s2)r=radius mt=time secm=mass…

Q: Show that a set of vectors V (not containing the 0 vector)is linearly dependent if and only if there…

A: Let’s consider the following sets of vectors,

Q: Find the following vector product A x ×F.

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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: Find the following vector product î x B.

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Q: Consider a cube with one corner at origin and the other corner along the body diagonal at (1,1,1).…

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Q: To find the vertical asymptote of a graph of a rational function, you set the numerator equal to…

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Q: Find D in cartesian coordinates) at P(6,8,-10) caused by a uniforms surfacecharge density p,…

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Q: Which of the following is the conserved quantity if the system having Lagrangian 1 (а) Р. (b) Р, (c)…

A: Lagrangian of a system is a function of generalised coordinate, first derivative of this generalised…

Q: Find the following vector product A x (F+2C ).

A: We can find the cross product of two vectors using the determinant of the matrix as given below. A =…

Q: Find each of the following in rectangular (a + bi) form if z = 2 – 3i; if z = x + iy. 22.

A: Given that  and we have to solve for

Q: The sum and difference of two vectors a and b are equal in magnitude. prove algebraically that the…

A: Two Vectors of 'a' and 'b' are equal in magnitude

Q: Q.1CC)IFE igen value of matrix is d, the corresponding eigen for matrix -882 vector is Lil 32 then d…

A: Given: The matrix is given as Let X be the Eigenvector matrix.

Q: Find each of the following in rectangular (a + bi) form if z = 2 – 3i; if z = x + iy. 21. z +1

A: z = 2 - 3 i

Q: If a regular polygon has 18 sides, find the measure of each interior angleand the measure of each…

A: Each interior angle of a n sided polygon will be given by following formula: Take n = 18…

Q: No matter what A and B, prove algebraically that A(A×B)=0

A: The vector C, C→=A→×B→=AB sinθ n^   Here, vector C is perpendicular to vector A and vector B.

Q: Show that the order of addition of three vectors does notaffect their sum. Show this property by…

A: If vector P and Q are at angle θ each other,   Consider vector A=3m towards east, vector B=4m…