r(t) = (t, sin t), t =

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

A: Given surfaces are z=x2x2+y2=4 Now, the equation x2+y2=4 represents a circle centered at origin with…

Q: Prove that the geodesic of a plane surface is a straight line using Euler-Lagrange Equation.…

A: We are to prove that the geodesic of a plane surface is a straight line using Euler-Lagrange…

Q: Find the parametric form of the equation of the line passing through the point Po(-2,-1,3) and…

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Q: 6. Write vector and parametric equations of the plane. a) parallel to the xz-plane and through the…

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Q: Let 7(t) = Find a parametric equation of the line tangent to r(t) at the point (106, 99,- 4.97) (t)…

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Q: Let F=-yi+xj and let C be a curve consists of the line segment C₁ from (0,0) to (4,0) followed by…

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Q: In exercises 5-8, information is given about a particle moving along a line in the xy-plane. Use the…

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Q: Exercise 2. Find a formula for the curve which is traced by the motion of a fixed point on a wheel…

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Q: Let the curve below be represented by the parametric equations: x- t- 12t , y-t?-2t over the…

A: Consider the curve  x=t3−12t,y=t2−2t              over −2≤t≤4

Q: 3. Determine vector and parametric equations for the plane through the point (1, -2, 3) and parallel…

A: Here we are given a point and perpendicular direction. We will express equation of plane in vector…

Q: (a) Graph u in the coordinate plane, with initial point (0, 0).   (b) Find the length and direction…

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Q: For cach of the exercises in this chapter, give a parametric description of the curve, and then…

A: The given equation is: x=sinπy  from 0, 0 to 0, 3 Usually sine graph will oscillates along x-axis.…

Q: 1. Let = 27-33+ k, (a) Normalize ü (find the vector that points in the same direction as u, but has…

A: We are given the vector v→=2i-3j+k. Our aim is to normalize the vector v, to find a non-zero vector…

Q: 3. Find the parametric equations of the tangent line to the curve: r(t) = sint i + (t²- cost)j + ek…

A: The given curve .The aim is to find the parametric equations of the tangent line at the point .