O Solve the electric flux through a paraboloid z =x² + y² – 16 that lies below plane z = 0. It is oriented by an outward unit normal vector with F = 3xî + 4yĵ – 5z²k.

Q: Find the arc length of the space curve given by the vector equation r(1) = (- 9t + 16) + (-9² +…

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Q: r(t) = (x(t), y(t), z(t)) where = - 4t? – 5t – 3 æ(t) - 5t2 + 5t + 3 y(t) = - 5t? z(t) : || Since…

A: Given a curve, rt=xt,yt,zt, where,  xt=-4t2-5t-3yt=5t2+5t+3zt=-5t2 Curvature of a curve rt, κ is…

Q: Sketch the space curve represented by the vectorvalued function                  r(t) = ti + (2t −…

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Q: Use Green's theorem to calculate the work done by force F on a particle that is moving…

A: This is a greens theorem problem

Q: The vector equation for the curve of intersection of the surfaces a = y? and z = y in terms of the…

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Q: Find a vector function, r(t), that represents the curve of intersection of the two surfaces. The…

A: Given:

Q: I can't find the tangential component of the acceleration

A: The given position vector is,

Q: Find the divergence of the vector i = xi + yj + zk. %3D (a) 0 (b)-3 (c) 3 (d)2

A: To find The divergence of the given vector.

Q: Sc (z² – 4|z| + Re(z) Y(t) = 2et, 0 <t< n/2. (iv) dz , where C is parametrized

A: Consider the given information. I=∫Cz2−4z+Rezdz As, γt=2eit,0≤t≤π2,  Let z be a complex number,…

Q: Given the f. conserrative :F(a,y)' Pind the work done to the while following vector Force field F,…

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Q: Find the flux of the vector field F across the surface S in the indicated direction. F= 6i+y4z8j-y…

A: According to the given information, it is required to find the flux of the vector field across the…

Q: Find the flux of the vector fleldF = (x – y*)i+ 4yj + x'k out of the rectangular solid [0, 1] x [1,…

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Q: Draw the graph of the vector-valued functions (a) for the plane curve, r(t) = 2cost³i + 3sint³j, 0<t…

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Q: Consider the ellipsoid 3x? + y? + z² = 11. The equation of the tangent plane to this ellipsoid at…

A: 3 x2 + y2+z2=11 and the point is (1,-2,-2)

Q: if A=i+j+X, B=zi-j+3ksfind vector normal to B and in plane of A and B- ans. $2(3i+9j+x)

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Q: Find a vector function, r(t), that represents the curve of intersection of the two surfaces. The…

A: Given two surfaces Z =   x2 + y2  and  plane z = 9 + y  We have to find vector function   r (t) We…

Q: A particle moves in the x – y plane with velocity v=(1-t)î +(4– 2t + t² )j where t is the time and i…

A: As per our guidelines we are supposed to answer only first three subparts of question at a time.…

Q: calculate the flux of the vector field through the given surface. ~F = ~i + 2x~j + 4y ~k, and S is…

A: GIVEN: F = i + 2xj + 4yk Surface, z = 2x2 + y + 3

Q: Evaluate fc F • dr, where F = (z, y2, x) and C is parametrized (in the positive direction) by r(t) =…

A: F=z,y2,x and C is the parametrized by r(t)=t+1,et,t2 for 0&lt;t&lt;2. We have to evaluate ∫CF·dr.

Q: Q1] Find a unit vector normal to the surface 3x2 у — узz? аt the point (1,-2, -1)

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Q: Find the postion vector R(t) given the velocity V(t)=(2t+2)i + 2sin(2t)j + 4t^3k and the initial…

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Q: Find a vector function that represents the curve of intersection of the two surfaces. The paraboloid…

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Q: Find a vector function r(t) that describes the curve of intersection between the elliptical cylinder…

A: given, elliptical cylinder 4y2+z2=4  and the plane x+y=1 we have to find a vector function r(t) that…

Q: The vector equation for the curve of intersection of the surfaces x = y² and z = y in terms of the…

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Q: Find the velocity and acceleration vectors in terms of u, and ug. de r= a sin 60 and 4t, where a is…

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Q: Find all points of intersection between the vector functionr(t) =⟨t, t2, t3⟩ and the plane defined…

A: Since the vector is contained in the plane, so all the points of the line intersect with the plane.…

Q: Let r(t)=(ln(t), t, (t^2)/2). Find the equation of the osculating plane corresponding to t= 1

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Q: Find the Vector function that represents the curve of the intersection of the two surfaces.  The…

A: Given equations are x2+y2+4z2=4 ..... (1) and x2+z2=1 ..... (2) From equation (1) z2=(4-x2-y2)/4…

Q: Find the velocity and acceleration vectors for the positionvectors are given in Exercises 30–32.30.…

A: 30. r(t)=t,t2,t331. r(t)=tet i , t ln t j32. r(t)=sec t, 1t, etln t

Q: Find the outward flux across the domain D xi + yj + zk x2 +y? + z? F(x,v,z) = across the sphere x2…

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Q: Consider the vector function $(t) = te“ i+ cos(t)j + k.Deter mine : a) ds/dt b)

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Q: Find a vector function that represents the curve of intersection of the paraboloid z = 2a² + 2y² and…

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Q: B) Find a vector parallel to the plane 2x – y – z = 4 and orthogonal to i +j+ k.

A: This is a problem of vector analysis.. we will solve the problem using the concept of vector dot…

Q: ). Determine the set Tp(Zf) of all tangent vectors to Zf at p. Is dim Tp(S) m ker d f.?

A: Sol

Q: A velocity vector of v = 3t²i – 6t³ j – 4k L is governing the movement of an object in the 3D space.…

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Q: 19. Suppose that the normal unit vector N of a surface S at z = f(x, y) is determined, how does the…

A: Note: As company policy, we solve first question only. Please resubmit the rest of the questions in…

Q: Find the value of a at which the plane curve traced out by the vector function E + bt> is not…

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Q: Find a vector function, r(t), that represents the curve of intersection of the The cylinder x² + y2…

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Q: Find the flux of the vector field F = (y, – z, x) across the part of the plane z = 3+ 4x + 2y above

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Q: Find a vector parallel to the plane 2x - y - z = 4 and orthogonal to i + j + k

A: Given:A plane 2x - y - z = 4 orthogonal to i + j + k

Q: Find a vector function, r(t), that represents the curve of intersection of the two surfaces. The…

A: We have to find vector function For this we have given equation of paraboloid and parabolic cylinder…

Q: Consider the curve r(t) = (t, 3 cos t, 3 sin t) for t 2 0. Is the integral o r(t)dt a number or a…

A: Given :   r(t) = ( t , 3cost , 3 sint )

Q: Find a vector function, r(t), that represents the curve of intersection of the two surfaces. The…

A: First solve the given equations for finding the values in terms of x

Q: e the electric flux through a paraboloid z = x² + y² – 16 that lies . It is oriented by an outward…

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Q: Let r(t) = (e²t, e−³,5t) Calculate the velocity vector and the acceleration vector at t = 0.

A: r(t) = ( e2t , e-3t , 5t ) given  find velocity vector and acceleration vector    velocity vector…

Q: Consider the curve F(1)=i +(/2 In(?))j + 1 -k. | а) Find the binormal vector B(1)

A: Given the curve  r→(t) = i→ + 2ln(t)j→ + 1tk→

Q: 1. Calculate the work done when a force F = 3xyî – y?j moves a particle in the xy-plane from (0,0)…

A: Take dot product along limit of integration and integrate

Q: Find a vector function, r(t), that represents the curve of intersection of the two surfaces. The…

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Q: Find the constants a, b, c so that the vector à = (-5x – 6y + az)i + (bx + y – 2z)j + (-3x + cy –…

A: Given the vector  A→=-5x-6y+azi→+bx+y-2zj→+-3x+cy-4zk→ Since the vector is irrotational the curl…