r(t) = (sin 7t, t, cos t)

Q: (9.) r(t) = (1, cos t, 2 sin t)

A: As per your query the solution of question no 9 is given the next step.

Q: or​ sphere, and show that the

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Q: Find the tangent, normal, and binormal vector functions for the following three curves:   curve 1:…

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Q: .3 At which point P does the curve r(t) = ( 2t have the tangent vector (24, -8, 3) ? (a) P(2, 2, 2)…

A: Here we have, the given curve is r→(t)=2t3, 2t2, 3t-1                now differentiate with respect…

Q: 4.a. Find the unit tangent and normal vectors to r(t) = 4 cost i + sin t j at t = /2. Sketch a…

A: Given that rt=4cost i +sin t j Then r't=-4sin t i  +cos t. The formula for tangent vector is…

Q: find the curve’s unit tangent vector. Also, find thelength of the indicated portion of the curve.…

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Q: Find the curve's unit tangent vector. T(t) = Di+Dj+Ok

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Q: Q1: for the position vector cos³ (t)i + sin³ (t)j, 0<t</2. Find the vectors T, N, B and the length…

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Q: The position vector of a particle moving along a helix is c(t) = (cos(t), sin(t), t²). (a) Find the…

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Q: Sketch the curve with the given vector equation. Indicate with an arrow the direction in which t…

A: To indicate the direction in which t increases and sketch the graph of the vector function given…

Q: Find the unit tangent vector and the length of the indicated portion of the curve: (a) r(t) = (6 sin…

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Q: Find the principal unit norma l r(t) = 6 cos ti + 6 sin tj + vector to the curve at the specified…

A: Given: r(t) = 6cost i + 6sint j To Find: Principal unit normal vector of the given position vector…

Q: Given the vector function (1) = (e+²³, 2√²³ +1, 4arctan(1 − 1)) 1)), find the speed and the equation…

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Q: 3. Find the curve's unit tangent vector and find the length of the indicated portion of the curve:…

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Q: 1. Given that r(t) = t²i+tj + 2k. Sketch the curve with the given vector equation. Indicate with an…

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Q: find the curve’s unit tangent vector. Also, find thelength of the indicated portion of the curve. .…

A: Given:                  rt=cos3tj+sin3tk,     0≤t≤π2                 v=ddtrt=ddtcos3t j+sin3t…

Q: Consider the given vector equation. r(t) = 3 sin(t)i + 4 cos(t)j (a) Find r'(t). r'(c) = (b) Sketch…

A: Solution of question is written in step2.

Q: 21. For the curve 7(t) = sin ti + cos tj, find 7 '(t) and sketch the position vector 7(÷) and the…

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Q: Find the length of the curve with the given vector equation. r(t) = cos ti+ sin tj+ 3t k; 0sts3

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Q: Find the arc length of the vector curve 7(t) = (2t, t², (1/3)t³), 0<t< 2.

A: Find the arc length of the curve

Q: (sin(t*), t, cos(t)) Answer the following for the curve defined by the vector function r(t) domain…

A: our objective is to find a formula for curvature ,length of the curve,unit normal vector.

Q: The position vector of a moving point is given as :R(t)=(cos t)i+(sint) j+(t) k ; the distance…

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Q: Sketch the curve with the given vector equation. Indicate with an arrow the direction in which t…

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Q: Find the unit tangent vector of the given curve. r(t) = 12t5i - 4t5j + 3t°k %3D

A: Given the vector function, r(t) , we call r′(t) the tangent vector provided it exists and provided…

Q: Determine the velocity vector of the given path. r(t) = (6 cos?(t), 3t – t3, 2t)

A: We have to find the velocity

Q: Find the curve's unit tangent vector. Also, find the length of the indicated portion of the curve.…

A:

Q: Dz: tow ord the find the unit vector Curve y =x? at

A: Find the unit vector towards the curve y = x2 at x= 1: r→t=xti^+ytj^y=x2:Let xt=t  and…

Q: The path r(t)=(5 sin t) i+(5 cos t) j describes motion on the circle x^2+y^2=25. Find the​…

A: We have to find ​ particle's velocity and acceleration vectors at t=π/3 and π/6 . Given  r(t)=(5 sin…

Q: A curve has vector equation r(t) = (In(sin t), In(cost),V2 E 0<t< T/2 Find an equation of the…

A: Given curve, rt=lnsint, lncost, 2t Point: -ln22, -ln22, π22 Equation of a plane passing through the…

Q: Find the tangent, normal, and binormal vector functions for the following three curves:   1:…

A: We have to find the tangent vector, normal vector and bionomial vector function

Q: 8. r(t) (sin Tt, t, coS Tt)

A: As per your query the solution of question no 8 is given in the next step.

Q: Given the vector function: 7(t) = (e', e' sin(t), e cos (t)) Determine the equations of the normal…

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Q: Let r(t) = (15, cos t, -3 sint) be the position vector of an object. Find the velocity and speed of…

A: Given that rt=15,cost,-3sint  find the velocity and speed of the object

Q: Given a curve C: r (t), find a tangent vector r (f), a unit tangent vector u'(t), and the tangent of…

A: Note: Since you have asked multiple question, we will solve the first question for you. If you want…

Q: find unit tangent vector of the given curve r(t)=(4-2t)i+(2t-3)j+(8+t^2)k

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Q: Find the curve's unit tangent vector. Also, find the length of the indicated portion of the curve.…

A: Given Data: Equation of Curve: r(t)=(cos3t)j(sin3t)k Interval: 0≤t≤π3 The derivative of the curve…

Q: Sketch the curve whose vector equation is r(t) =

A: given rt=&lt;tcost,tsin,t&gt;

Q: 2. Let C be a curve given by r(t) = (e' sin t, e' cos t, /2e'), t is real. (a) Find the binormal…

A: Given, r(t)=etsin t, etcos t,2et

Q: Q1: For the position vector r = et cos(t) i+ et sin(t) j+ e¯tk, find the velocity and acceleration…

A: Note : There are many questions in the above image. So I will answer the first question and…

Q: Find the curve's unit tangent vector. Also, find the length of the indicated portion of the curve.…

A:

Q: Q1: For the position vector r = et cos(t) i + et sin(t) j+ etk, find the velocity and acceleration…

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Q: find the curve’s unit tangent vector. Also, find thelength of the indicated portion of the curve.…

A: Vector: r=(6 sin 2t)i + (6 cos 2t)j + 5tk =&gt;v=drdt=12cos (2t)i-12sin(2t) j+5k…

Q: Find r′(t), r(t0), and r′(t0) for the given value of t0 = /2. Then sketch the curve represented by…

A: r( t ) = 3 sin t  i→+ 4 cos t  j→r( t0 ) = 3…

Q: Given the vector function (1) = (e+→¹², 2√³+1, 4 arctan(1-1)), find the speed and the equation of…

A: Introduction: Like two dimensional Euclidean geometry, a line can also be drawn in three dimensional…

Q: Sketch the curve with the vector equation ř(t) = (sin t, t). Indicate with an arrow the direction in…

A:

Q: Sketch the curve with the given vector equation. Indicate with an arrow the direction in which t…

A: The given vector equation is

Q: At which point P does the curve r(t) = ( 21, 4t +1, t) given in vector form have the tangent vector…

A: