For the particle in a box, show the wave functions w, NTTX sin - for n=3 and n=6 are normalized and orthogonal.

Q: The equation of the tangent plane to this ellipsoid at (1, –2, –2) is The vector parametric form of…

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Q: Consider the helix r(t)=(cos(3t), sin(3t), 3t). Compute, at t=π/6 The unit normal vector N

A: The given vector of helix is,

Q: The position of a particle moving in space at time t>=0 is r(t) = 2i + (4 sin t/ 2) j + (3 -…

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Q: Express the given parametrization in the form y f(x) by eliminating the parameter. - In(t), y = 5 +…

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Q: Find the open interval(s) on which the curve given by the vectorvalued function r( ) = 2 cos3 i + 3…

A: Consider the given vector-valued function: Here the objective is to find the open intervals on…

Q: Let C be the line segment from [1 – i,2+ 2i). (a) Parametrize C. (b) Integrate 2 over C.

A: According to the given information, Let C be the line segments from [1-I,2+2i]. For part (b) it is…

Q: The magnetic field along a solenoid is conservative and given by 2xy 7- (2 x ₁-2x, (x²+1)-2). ¡−2x,…

A: Given a vector field as F=2xyx2+1-2x,lnx2+1-2 We need to find the scalar potential from which this…

Q: Show that f(x, y) =(Aekx + Be-kx )(Ce2ky + De−2ky) is a solution of the wave equation ∂2f/∂y2−…

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Q: Calculate the arc length of the following vector function. E(1) = 4 In i+j+ 4t k; 1sts2.

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Q: A vector field v is expressed in spherical coordinates as v(r, 0, 0) = 2r sin cos o e, +r cos o cos…

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Q: Sketch the curve represented by the vector-valued function                               r(t) = 2…

A: Given information: Vector-valued function rt=2costi+tj+2sintk trigonometric identity, sin2t+cos2t=1…

Q: An elastic string which is fixed at both ends is governed by the wave equation a²u a?u 0 0, at2 əx²…

A: Let us consider the wave equation ∂2u∂t2=∂2u∂x2, 0≤x≤1, t≥0 and L=∆x=0.25; K=∆t=0.1 Consider x=ih…

Q: Find the tangential and normal components of accelerationfor a particle moving along the circular…

A: We know that, tangential and normal components of acceleration for a particle moving along the…

Q: Show that ¥(x,t)= Asin(wt+kx) describes a wave motion

A: Given: ψx,t=Asinwt+kx

Q: The magnitude of the x-component of a unit vector at the point (1, 1) that is normal to $(r) : equi-…

A: The formula to calculate the vector which is normal to the equipotential  line of the potential…

Q: The normal component of the acceleration vector for an object with position vector r(t) = (cos(t),…

A: To check the given statement for True/False.The normal component of the acceleration vector for an…

Q: A vector field v is expressed in spherical coordinates as v(r, 0, 6) = 2r cos 0 e, – r sin 0 eg.…

A: For the solution follow the next step.

Q: Find the tangential and normal components of acceleration for 7(t) = < 5 cos(t), 3t, 5 sin(t)…

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Q: Solve the wave equation on the half line with the Utt – cʻuxx = 0, x> 0, t > 0 и, (0, 1) %3D h(),…

A: Given the wave equation is                     utt-c2uxx=0,   x&gt;0, t&gt;0ux(0,t)=h(t),…

Q: ii) Evaluate the vector line integral of F, F. ds, where y is an oriented curve defined as follows:…

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Q: 3. Verify that u(r,t) = sin(r - at) satisfies the wave equation:

A: To verify that ux, t=sinx-at satisfies the wave equation ∂2u∂t2=a2∂2u∂x2

Q: Find the velocity and acceleration vectors in terms of u, and ug. de r= a cos 20 and 5t, where a is…

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Q: Let the the position vecor be R(t) = (e' cos(3t) , e' sin(3t),0). Compute the unit tangent vector

A: The given position vector is R(t)=etcos(3t),etsin(3t),0 . compute the unit tangent vector T(t)=?

Q: Compute the tangent vector to the given path. c(t) = (4t sin(t), 6t) %3D

A: The tangent vector for a vector r→t is r→'t.

Q: Find the normal component, aN, of the cceleration vector of a particle moving in -space with…

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Q: he vector field at the given point F (x, y, z) = e* sin yi – e

A: Here we have to find the curl F for the vector field at the given point (0,0,1)   we have,…

Q: nd the unit normal vector N to the clothoid r(t) = (> x(1) = du sin 3 3 y(1) = / cos cos du 3

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Q: Verify that the function u(x, t) = (r – at)° + (x + at)° satisfies the wave equation uu =

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Q: In 3 [te' i + e'j + In tk] dt 1

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Q: Show that the vector field F = i + sin(z) j + y cos(z) k is conservative and then find the…

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Q: The equation of the tangent plane to this ellipsoid at (1, –2, –2) is The vector parametric form of…

A: Let's find.

Q: Show that the vector-valued function r(t) = ti + 2t cos tj + 2t sin tk lies on the cone 4x2 = y2 +…

A: Given: Vector-valued function: r(t)=ti^+2tcostj^+2tsintk^ Cone: 4x2=y2+z2

Q: Find the velocity and acceleration vectors in terms of u, and ug. r= a(7 - cos 0) and de =7, where a…

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Q: Use a parametrization to find the flux n do across the surface in the given direction.

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Q: Find the velocity and acceleration vectors in terms of u, and ug. de r= a(7 - cos 0) and = 6, where…

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Q: Let the position vecor be R(t) (3t, 2 cos(3t), 2 sin(3t)). Compute the principal unit normal vector…

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Q: Find the acceleration of a particle having position function r(t) 6 sin ti+ 9t j+ 2 cos t k

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Q: Find the principal unit normal vector for the helix r(t) = 2 cos ti + 2 sin tj + tk.

A: Given, r(t)=2 cost i+2 sint j+t k

Q: Find the position vector for a particle with acceleration, initial velocity, and tinitial position…

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Q: Show that the vector field ? = ? + sin(z)? + ycos(z)? is conservative and then find the…

A: We have to show that the vector field F=i+sinzj+ycoszk is conservative and then find the…

Q: The unit tangent vector of a(t) =cos 2t e, +stn 2t e, - tez at t = is

A: A vector is a quantity that has both magnitude and direction. It can be also defined as the…

Q: Consider a particle moving on a circular path of radius b described by               r(t) = b cos…

A: Given position vector is rt=bcosωt+bsinωt.

Q: Consider the vector of electric field Е(х, у.2) %3 (sinh x)1 - (сosh y)) — хуг k a. Compute the…

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Q: Which of the following represents the arc length of the vector function r(t) = (sin 2t, e, ) on the…

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Q: Find the velocity and acceleration vectors in terms of u, and ug. de r= a cos 30 and = 4t, where a…

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Q: Find the open interval(s) on which the curve given by the vector-valued function is smooth r(0) = 4…

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Q: Consider a vibrating guitar string of length L = 648mm that satisfies the wave equation Uxx = Utt, 0…

A: Given below clear explanation