2. Let a(t) = (3t – t³, 3t², 3t + t³), for t e R. (i) Calculate the equation of the osculating plane to a at t = 1. (ii) Calculate the curvature of a. 111 Calculate the torsion of a.

Q: Find the curvature k for the space curve r(t) = (4 +t)i + tj. %3D Lütfen birini seçin: a. 3/2 b. 2…

A: Given curve is Applying derivative: Applying derivative again:

Q: Find the curvature of the plane curve at the given value of the parameter.           r(t) = t2i + j,…

A: We have given the curve  r(t) = t2i + j, t = 2

Q: Find the curvature of the plane curve at the pointindicated. y = e^t , t = 3

A: y=et,  t=3 Differentiating with respect to t, we get dydt=et Again differentiating with respect to…

Q: Find the curvature of the plane curve at the point indicated. y = t^n, t = 1

A: First find the first and second derivative of the given curve…

Q: Find the equation of the tangent plane at the point T(1,1,4) of the sphere (x – 1)2 + (y – 2)² + (z…

A:

Q: 3. (a) Find the curvature (t) for the vector-valued function (t², 2t, In t), t > 0. (b) Find where…

A: Basic identities of differentiation and vector calculation are used

Q: 3. Find the curvature of the plane curve (t, t") at t = 1.

A: see below the answer and calculation as per bertleby guideline I have to solve only 1 question. For…

Q: 1) Calculate the curvature of the position vector r(t) = sin tāx + 2costāy + V3 sin tāz is a circle,…

A:

Q: TU? TU? r(t) = (/ * du, sin -du ) , t > 0 COS 2 2

A: r(t)=∫0tcosπu22du,∫0tsinπu22du,t>0 We have to find the unit tangent vector T and Curvature K for…

Q: (b) Given that r(1)=(r.r.) Find the curvature of r(t) at the point P(2,4,2).

A:

Q: Find the curvature of the space curve. r(t) = -10 i + (t + 4) j +(In(cos t) +9) k %3D OK= sect K =…

A: Formula of radius of curvature:      k=r→'(t)×r→''(t)r→'(t)3 First we need to find r→'(t),r→''(t),…

Q: Find the curvature of the curve C: r (t) = (e, e', 2t) at t = 0

A:

Q: Find the curvature of the space curve. r (1) = -8i + (1 + 4) j + (8 + In(cos t)) k %3D OK = sec t…

A:

Q: Find the curvature of the plane curve at the given value of the parameter.          r(t) = ti + 1…

A: Given data: *The plane curve is  r(t)=ti+19t3j *The value of the Parameter is t=2. The derivative of…

Q: Consider the helix r(t)=(cos(3t),sin(3t),−1t). Compute, at t=π/6:  A.The unit tangent vector T= (…

A:

Q: Show that along the plane curve x = #1(t)e, +2(t)e2 the curvature is 4.30. [(a)2(5)213/2 a0 + 3

A: The curvature K at a point of a curve defines the speed of rotation of the tangent of the curve at…

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: 2. Calculate the curvature, unit binormal vector and torsion for r(t) (e'cost)i+(e'sint)j +5k

A:

Q: Find the curvature and radius of curvature of the plane curve at the given value of x. y = e X/4, x…

A: Given y =e^(-x/4)  ,x=8 Now we have to find curvature and radius of curvature at x=8

Q: If r(t) = , then unit tangent is a principal unit normal is a and its curvature is a vector scalar

A: Explained below

Q: The curve in the figure below is parametrized by F(t) = (t³ – 3t) · i + (3t² – 2) · j, for -00 <…

A: Here, the given parametric curve is: r→(t)=(t3-3t) i +(3t2-2) j

Q: A particle Q is moving along a position vector, r(t) stated as r(t) = (6 sin t)į + (6 cos t)j + 8tk…

A:

Q: 1) Calculate the curvature of the position vector r(t) = sintāx + 2costāy + V3 sin t āz is a circle,…

A: Given position vector is  r→t=sintax→+2costay→+3sintaz→ Then unit tangent vector is…

Q: Find the curvature for the following vector function. 1. r(t)=( 4t, -t², 2t³)

A:

Q: 1. Consider the position vector r(t) = (t³) i + (3t) j + 4k and at t = 1 find the: (a) curvature,…

A: The general form of the parametric equation of the curve in three dimensional space is given by ,…

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 +…

A:

Q: Find the curvature of the given curve r(t) = 5ti +3sin(t)j + 3cos(t)k a. 2//34 b. 4//34 C. 3/34 d.…

A:

Q: 2. Consider the following vector function: r(t) = = a cos wti + a sin wtj + bwtk, where a, b and w…

A: We need to find radius of curvature.

Q: Find the curvature of r(t) = at the point (1,0,0)

A:

Q: Find the curvature of the plane curve y=2t^4 at the point t=2 κ(2)=

A: The given curve y=2t4

Q: Show that if r(t) is perpendicular to the tangent vector r′(t) for all t, then the curve r(t) lies…

A: If r(t) is perpendicular to the tangent vector r′(t) for all t, then the curve r(t) lies on a sphere…

Q: 1) Calculate the curvature of the position vector F(t) = sin t ax + 2cost ay + V3 sin t āz is a…

A: Formula of Curvature(K) of the position vector r(t):…

Q: 8. Find the curvature of the vector-valued function r(t) = at the point t = -1.

A: given function is rt=3t2,-4t,1t find the curvature at t=-1 k=r→'t×r→''tr→'t3

Q: Find k (curvature) and t (torsion) for curve C represented by F(t)=(e^t,-e^t,(2t)^1/2)

A:

Q: 2. Let a(t) = (3t-t, 3t2, 3t + t), for te R. %3D (i) Calculate the equation of the osculating plane…

A: Introduction: The formula of curvature of and torsion is given by, κ(t)=α"(t)…

Q: Determine the curvature of r(t) = t^2 i+ t k

A: In this question we have to find the curvature of the vector which we can find out by using the…

Q: Given r(t) = 2e"i+(2e² cost) ost)j+(2e* sint)k . Evaluate T(1), N(1), binormal vector, B(t), and the…

A:

Q: Determine the curvature at any point on the curve given by R(t) = i +t?j+t³k. %3D

A:

Q: Let F(t) = (t2 – 1, 2t, 2t2 + 3). a) Find limo K(t). b) What is the point of maximal curvature? c)…

A: We will use r'(t) and r"(t) to find answer all part

Q: Find the curvature of the vector-valued function. r(t) = (e3t,e)

A:

Q: Show that for a plane curve the torsion T = 0.

A: We have to shown that, For a plane curve the torsion T=0

Q: ; Consider the vector function r(t) = ti + t²j+t°k. Compute the curvature of r at time t = 2.

A: Hello. Since you have posted multiple questions and not specified which question needs to be solved,…

Q: #3. Use the cross product formula to calculate the curvature of the following vector function. r(t)…

A:

Q: Consider the helix r(t)=(cos(2t),sin(2t),−4t)r(t)=(cos⁡(2t),sin⁡(2t),−4t). Compute, at t=π6t: A.…

A: Given r(t)=cos2t , sin 2t   , -4t      ; t=π6

Q: find the curvature of the plane curve at the given value of the parameter. r(t)=4ti-2tj,    t=1

A: To find- curvature of the plane.

Q: Find the gaussian and mean curvature functions of the surface m given by the equation y3=y1y2 in R³…

A: First parameterized the equation.

Q: Find the curvature of the plane curve. 13. r(t) =t² i+ j t = 2 14. r(t)=(t, sint) at t =- 2

A: 1)

Q: For a plane curve r(t) = (x(t), y(t)), |æ'(t)y" (t) – x"(t)y' (t)| (x'(t)² + y' (t)²)³/2 - k(t) Use…

A: Here we have to use this equation to compute the curvature at the given point.