5. Sketch the curve r(t) =< sint+2 sin(2t), cos t— 2 cos(2t), – sin(3t) > (you can plot it in Geogebra first and then transfer on to paper). Can you calculate the vectors T, B and N at t = 0 and at t = 2π?

Q: Find the unit tangent vector to the curve defined by F(t) = (4 cos(t), 4 sin(t), 3 sin²(t)) at t = 3…

A:

Q: How do the paths r1(t) = (cost,sin t) and r2(t) = (sin t, cost)around the unit circle differ?

A: Given :                   r1(t) = cos t , sin tr2(t) = sin t , cos t

Q: Find parametric equations for the tangent line to the curve x=cos⁡(t), y=sin(⁡t), z=t at the point…

A:

Q: Evaluate √(2² + yz sin(xyz))dx+(y²+xz sin(xyz))dy+(x+xysin(xyz))dz where C is the curve following…

A:

Q: Question 2. Which three of these vector functions trace out the same curve? (a) r(t) = (−2+ cost)i +…

A: As per the question we are given five parametric equations in form of vector valued functions. And…

Q: The curve of the vector r (t) = (20 cos t + 10 cos 5t, 20 sin t + 10 sin 5t) over 0 <t< 2n is shown…

A: The curve of the vector  .

Q: Write the parametric equations x = = 5 sin² 0, y = 3 cos² 0 e given Cartesian form. 3sqrt(1-x^2/25)…

A: Given query is to find the Cartesian equation.

Q: Find parametric equations for the tangent line to the given curve at the point (30, 135, 469). The…

A:

Q: 5. Find the parametric equations of the line tangent to the curve C defined by the vector equation…

A: To find the parametric equation of the given tangent to the curve. The vector equation of the curve…

Q: The curves 71(t) = (- 5t, t°, 3t*) and r2(t) = (sin(5t), sin(2t), t) intersect at the origin. Find…

A: Answer

Q: Find the derivative, r'(t), of the vector function. r(t) = t* i + cos(t³) j + sin?(t) k

A:

Q: Find the unit tangent vector to the curve defined by F(t) = (4 cos(t), 4 sin(t), 3 sin (t)) at t = 3…

A:

Q: Find the length of the curve r= 1+ sin(20) Oses- /20

A:

Q: Question 1 described by the vector function r(t) = (4t² ln t, ¹-4, -2e-3t). 2 a) Consider the curve…

A: Given: Vector function rt=4t2lnt, t-42, -2e-3t. a. To find the integral ∫rtdt. b. To find the…

Q: iez3 dz. ty z – i

A: In this question, we need to find the value of complex integral. Here first we find the contour and…

Q: 7. Calculate dy/dx at the point indicated: f(0) = (7tan O, cos O), 0=/4

A: Here we will use the concept of parametric equation and Derivative of parametric ewyations

Q: The parametric equations of a curve is x = 3 sin t, y=3 cos t and z = 4. (a) Sketch the curve r(t)…

A:

Q: 1. The parametric equations for the astroid below are x = sin' (t), y =- cos (1) on 0<t < 2a. a)…

A: Given, the parametric equation for the astroid below are  First need to find the stating point on…