1. Let R and b be positive constants. The vector function r(t) = (R cost, R sint, bt) traces out a helix that goes up and down the z-axis. a) Find the arclength function s(t) that gives the length of the helix from t = 0 to any other t. b) Reparametrize the helix so that it has a derivative whose magnitude is always equal to 1. c) Set R = b = 1. Compute T, N, and B for the helix at the point (√2/2, √2/2, π/4).

Q: For the curve R (t) = (Sin2t, t, cosat) Find the unit tangent vector.

A:

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

A:

Q: Let F(t) = (1, ²,4) and P = (2, 10, 4). Consider the curve C parametrized by F(t). Compute a tangent…

A: The objective of the question is to find the tangent vector, unit tangent vector, and the tangent…

Q: 1. Let ř(1) = . Find a vector and parametric equation of the line tangent to F(1) at the point (-…

A:

Q: 3. Consider the following helix with vector equation 7 (t) = 2 cos (t) 7 (t) 7 + tỉ + 2 sin (a)…

A:

Q: 4. Let r(f) = ° 13 i - 6fj + Pk. (a) Find the unit tangent vector T(t) and T(3). | (b) Find the…

A:

Q: Ifr(t) = (sin t , cos t, 29- t), then determine a vector that is perpendicular to both unit tangent…

A: Given: r(t) = sin t, cos t, 29-t To determine: A vector that is perpendicular to both unit tangent…

Q: 2. For this entire page, let r(t) = (4 sin(t), 3t, 4 cos(t)) (a) Circle the correct graph for the…

A: The objective of this question is to understand the properties of the vector function r(t) = (4…

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

A:

Q: Q2) consider a particle moving in a curve defined by F(t) =sin 21, cos 21, 1. Find a. The velocity…

A:

Q: Let r(t) = (-3t5 - 1, 2e³, 4 sin(4t)) Find the unit tangent vector T(t) at the point t = 0 T(0) -

A: If  is vector valued function which is differentiable and then the unit tangent of is given by

Q: b) Find Unit vector tangent and normal to the y=x² at P(²₂4) curne

A:

Q: For the curve defined by F(t) = (e¯', 4t, e') find the unit tangent vector, unit normal vector,…

A:

Q: tangent plane

A:

Q: 2) Let r(t) = (t, t² , e'). Find an equation for the unit tangent vector T(t).

A:

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

A: To find the unit tangent vector.

Q: A fire ant, searching for hot sauce in a picnic area, goes through three displacements along level…

A: Since you have posted multiple questions. I am answering the first three sub-parts. Please post the…

Q: Calculate the velocity and acceleration vectors, and speed for when t = Speed: 11. Velocity:…

A: To calculate the velocity and acceleration vectors, and speed for .

Q: Let P be the point (2, -1, 2) and Ø,: x² + y² – z² = 10. (i) Find the unit normal vector to the…

A: (c) The given surface is ∅1: x2+y2-z2=10 and the point P: 2,-1,2. (i) The unit normal vector to the…