18. Determine the values oft between 0 and 27 such that the tangent vec- tor to the cycloid r(t) = (t - sin t, 1 - cos t) is a unit vector.

Q: Q2. A particle is moving along the curve whose position vector is given as R(1) = (1) i + ( In…

A: Given

Q: Find unit tangent vector of the curve r=(2+t)i-(t+1)j+k

A: In this question, we need to find the unit tangent vector of the given curve.

Q: 2. Find the unit tangent vector for the curve r(t) = (t cost, tsin t).

A:

Q: 3. Let the curve C be traced by the vector-valued function R(t) = cos(at) î + at j+ sin(rt) k. %3D…

A:

Q: Find a tangent vector of unit length at the point with the given value of the parameter t. r(t) = 2…

A: We differentiate the given equation with respect to t.  r(t) = 2 sin(t)i + 9 cos(t)jr'(t)=ddt 2…

Q: Find the unit tangent vector to the curve at the specified value of the parameter. r(t): = 7 cos(t)i…

A:

Q: If an object follows the path of the two-dimensional vector-valued function p(t)=(16−cos(t),…

A: Given p(t)=(16−cos(t), 0.6πt−0.15t2−3)

Q: 6. Determine the values oft between 0 and 27 such that the tangent vector to the cycloid r(t) = (t –…

A:

Q: Sketch the graph of 7(t) = sin(t)i – 2cos(t)j–tk in 3-space; then find and draw the tangent vector…

A: Given, r→t=sinti^-2costj^-tk^

Q: 3. Find the unit tangent vector at t = T/2 for the following parametrized curve: F(t) = (cos 2t, 4,…

A: The given parametrized curve r→(t)=cos2t, 4, sin2t

Q: How would I find the unit tangent vector T(t) at the point with the given value of the parameter t.

A:

Q: Find the unit tangent vector to the curve at the specified value of the parameter. r(t) = 3 cos(t)i…

A:

Q: 10. Find the unit tangent vector to the curve below at t=r/3 r(t)=sin ti+Cos tj+tan tk

A: We have to find the unit tangent vector to the curve at t=pi/3.    r(t)= sin2ti + cos2tj + tan2tk .

Q: Find a vector equation for the tangent line to the curve 7(t) = (5 cos(6t))i + (5 sin(6t)) j +…

A:

Q: 2. Find thé moving trihedral of the curve C traced by the vector-valued function R(t) 4 cost i+4…

A:

Q: Find the unit tangent vector of the given curve. r(t) = (7- 2t)i + (2t - 3)j + (6 + t)k 2 1 O A.…

A:

Q: Let C be the curve of intersection of the paraboloid x? + y² = z and the cylinder + (y – 1)² = 1. 4…

A: We will find equation of common curve and parametrize it to find vector equation of C and the use…

Q: Find the vector equation of the tangent line to the curve given by 7(t) = sin ti + cos (2t)j + tan…

A: There is no such introduction for the solution.I have explained it within the solution.Please go…

Q: Find the unit tangent vector T(t) to the curve r(t) 2 = (, sint – t cos t, cos t +t sint), t> 0,

A:

Q: Find the vector equation of the tangent line to F(e) = 2 (e1-t) in t i + tan"1tj+ k at cos(t ) the…

A: To determine the vector equation of the tangent line.

Q: Find the unit tangent vector of the curve r(t) = (1 + 3 cos t)i + (3 sin t)j + t2k

A: Find the unit tangent vector of the curve.

Q: b) Find the unit tangent vector for.. r(t) = at t=0

A: The unit tangent vector can be calculated using the formula T→(t)=r→′(t)‖r→′(t)‖. The denominator is…

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: 4. Find the unit tangent vector T(t) for the vector function: r(t) = .

A: To find the unit tangent vector.

Q: 3. Let C be the space curve given with the vector valued function R(t) = (1+2 sin(2nt))i+ (In t)J +…

A:

Q: Next Consider the two vector-valued functions given by r(t) = (t+1, cos 1+t w(+) = (*, sin() *) . a.…

A: (a) The two vector valued functions intersect if r(a) = w(b) for some t = a and s = b.…

Q: At which point P of the curve defined vectorially with r (t) = (21, 4t + 1, t) is the tangent vector…

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

Q: 3. Let the curve C be traced by the vector-valued function R(t) = cos(at) î + at j + sin(at) k. Find…

A:

Q: 2. For a non-zero vector ü(t), show that 1 dü dt u| dt dû dt where û is the unit vector in the…

A: Let u→ be the vector and |u |→ is the magnitude of u.→ unit vector u⏜ is given by:  u^=u→|u→|…

Q: 9- The unit tangent vector T(t) = (- sin ti + cos tj+3k) is given. Using definition of unit normal…

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

Q: Let r(t) = te'i + (t – 3t)j+ (sin 4t + t)k. Find the unit tangent vector at the point where t = 0.

A: To find unit tangent vector at t=0 Initially we want to find derivative of the vector at t=0 and…

Q: 1. Given the vector-valued for R(t) = (2 sin 2t-1)i+ 2 cos 2tj+ 3tk. %3D (a) Find the length of the…

A: Given that Rt=2sin2t−1i+2cos2tj+3tk

Q: Find the unit tangent vector T(t) at the point with t = 0 where r(t) = cos(t) i + 3t j + 2sin(2t) k…

A: We first find r'(t) by differentiating both sides with respect to t. And plug t=0 r(t) = cos(t) i +…

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 tangent vector at t= In 2 for the following parameterized curve. r(t) = 5 e'i+e -2tj+6 e 2k…

A: Explanation of the answer is as follows

Q: Find a tangent vector of unit length at the point with the given value of the parameter t. r(t) =…

A: Given, r(t)=(1+t2)i+t2j To find the unit tangent vector at the point t=1.

Q: 1. Find the unit tangent vector to r(t) = at t = n.

A:

Q: Find the unit tangent vector to the curve at the specified value of the parameter. (-)- II r(t) = 3…

A:

Q: 1. Find the tangent vector to the curve 6t r(t) = [t³ – t, t+1 , (2t + 1)*] at t = 1.

A: As per our guidelines we are supposed to answer only one question. If you want solution of any…

Q: Find the vector equation of the tangent line to F(t) = 2 (e-) in t i+ tan-tj+ the point where t = 1.…

A:

Q: Find the unit tangent vector for the curve C given by R(t) = cos³ ti + sin³ t j + 2k.

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

Q: Find the unit tangent vector T (0) to the curve C: r(t) = 4 sin(t)i +2 cos(t)j+ 3tk

A: We have to find T(0)

Q: 3. Compute the tangent plane at u = 0 and v=0.

A: Introduction: The formula of the tangent plane of the function f(x,y) at the point a,b is given by,…

Q: find the tangent line to the vector function at the given point. 7(t) - cos (4 t) i+3sin(4t)j+tR at…

A:

Q: Let 7 (t) = (3t3 + 4, – 4ešt, – 5 sin(4t)) - Find the unit tangent vector T (t) at the point t = 0…

A:

Q: Find the unit tangent vector T(t) at the point with the given value of the parameter t. r(t) = (2 -…

A:

Q: 1. Find the tangent vector to the curve 6t r(t) = [t° – t, (2t + 1)*] at t = 1.

A:

Q: Find the unit tangent vector to the curve defined by T(t) = (3 cos(t), 3 sin(t), 5 sin (t)) at t = 3…

A:

Q: (b) Given the vector-valued function r(t) = 4 cos t i + 4 sin t j. Calculate its unit tangent vector…

A: see below the answer