For the trivial line bundle E over the manifold M = R onsider the connection 1-form w =-xzdt + (x² – yr)dx + (x +zt?)dy+(z²t – y)dz. Compute the curvature 2-form F = -dø and show dF =0

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Q: Let C be a circle lying in the plane x+ z = 2 with center at (1,0, 1). Evaluate the line integr V2…

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Q: Q2/ Find T, N, and k for the space curve r(t) = (3 sin t)i +(3cos t)j + 4tk

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Q: Let P = ( 0 , 0 , 2 ) and let S be the unit sphere with equation x2+y2+z2=1. The collection of…

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A: We have to find the curvature of the curve r→(t)=2+5t, 5-t, 4-2t at the point t=-3 .

Q: a) Start by finding a single vector function that represents the intersection of the surfaces z = y?…

A: (b) Starting by finding a single vector function that represents the intersections of the surfaces…

Q: Find the curvature of the space curve. r(t) = -10i + (t + 6)j +(ln(cos t) + 7)k x = sin t x = csc t…

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Q: A: Find the distance from the point (2,2,3) to the line x=1+t,□( ) y=3-t,□( ) z=2t.

A: As per bartleby guidelines only 1 question is answered please upload the rest separately. The line…

Q: Find the curvature of the space curve r(t)=(t+4)i + 9j + (In(sect) +3)k answers:  A)cost B)sect…

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Q: b) Calculate dz z² - 1 S ₂ Along the positive direction of the curve |z| = 2 Hint: The curve |z| = 2…

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Q: Let P, Q be two points on the sphere of radius 1. Assume that P ≠ -Q. Show that there exists a curve…

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Q: Find the curvature of the curve r(t) (2t +9) i 10 j + (4 - 1t 4) k %3D 1 K = 21+12 1 + t2 1 к 21 +…

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Q: 1.Solve the following polynomial equations.  a)  2X3+1=x2+2X

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Q: 2. Consider the line r(t) = (4t+1,3, 2 - t) and the ellipsoid + + z? = 1. What is the distance from…

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Q: Find the curvature k of the circle C:(x – 2)2 + (y +3) = 25 - at the point (5, 1).

A: circle equation is x-22+y+32=25 and point 5,1find curvature k

Q: Q. find the curvature K of each plane curve traced out by the vector function r=r(t) = (3t – t3)i +…

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Q: Find the curvature of the space curve. r(t) = - 3i + (3+2t)j + (t +8)k %3D

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Q: 3. Find the moving trihedral and the curvature at any point of R(t) = (In(sect), t/V2,t/V2). %3D

A: Introduction: In differential geometry, the Frenet–Serret formulas define the kinematic properties…