
Choose the graph that matches the vector equation. r(t = - i + j + tk,...
Choose the graph that matches the vector equation. r(t) = – ti + tj + tk, Osts 1 Choose the correct answer below. A. B. C. D. Az AZ (-1, 1, 1) (1, 1, 1) 1 A у X X X |(1, 1, -1) X
1. Consider the curve i(t) = (t sin(t) + cos(t))i + (sin(t) – t)j + tk. (a) Find the length of the curve for 0 <t<5. (b) Is the curve parameterized by arc length? Justify your answer. (C) If possible, find the arc length function, s.
QUESTION 4 Given the equation of a point, r(t) ( I)i ( -I)j Sketch the graph of r(r) = (1 + l)i + (r2-Dj fr-2 2. Draw the (a) t 4 marks) position vector r(0) on the same diagram. b) Find the unit tangent vector of the point at 0 and show it on the same diagram in (a). Explain what you understand about the direction of the tangent (5 marks)
13.4.1 TT ht Find T, N, and k for the plane curve r(t) = 2+ i +2 In (cost)j, - 3<t<z
(1 point) Find a vector equation for the tangent line to the curve r(t) = (2/) 7+ (31-8)+ (21) k at t = 9. !!! with -o0 <1 < 0
(1 point) Find the length of the curver r(t) = i +3t'j + tºk, 0<t</96 L
PLEASE ANSWER THIS QUESTION CORRECTLY AND
ASAP!!!
What is the domain of the vector function r(t) = <2t+2, V3 –t, In (t) >. O a) {t]–3<t<0} b) {t|0<t<3} c) {t\t<3) d) {t|0<t <3} e) {t-3 <t<0}
4. Let C be the closed curve defined by r(t) = costi + sin tj + sin 2tk for 0 <t<2n. (a) [5 pts] Show that this curve C lies on the surface S defined by z = 2.cy. F. dr (b) (20 pts] By using Stokes' Theorem, evaluate the line integral| " where F(t,y,z) = (y2 + cos z)i + (sin y+z)j + tk
2. Determine whether there is a potential function for the vector field V= <yz, xz, xy>. You may use any legitimate method but you must justify your claim. If it there is a potential function, then find it and use it to evaluate the line integral scv. dr along the curve r(t) = <vt, t - 4,t +1> for Osts 4.[10]
Using Mathematica Consider the vector-valued function r(t)=et cos t i+(sin t)/(t+4) j +t k. a) Plot the curve with t going over the interval [-2, 2]. b) Plot the curve again over the same interval, but this time add the velocity vector in blue at (1, 0, 0) to the graph. c) Plot the curve again over the same interval, along with the blue velocity vector at (1, 0, 0), but this time add the acceleration vector in red at...