8. Find the length of the curve given by F(t)=(3 sin(21),19,3cos(21), for ISIS 3, rounded to...
3. (5 points) (a): Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x=etcost, yr etsint, z=et; (1,0,1) (b): Find the unit tangent vector T, the principal unit normal N, and the curvature k for the space curve, r(t) =< 3 sint, 3 cost, 4t >.
Find the curvature of the curve defined by F(t) = 227 + 5tj K= Evaluate the curvature at the point P(54.598, 10). Find the Tangent vector, the Normal vector, and the Binormal vector (T, Ñ and B) for the curve F(t) = (4 cos(5t), 4 sin(5t), 2t) at the point t = 0 T(0) - N(0) = BO) - Find the Tangent, Normal and Binormal vectors (T, Ñ and B) for the curve F(t) = (5 cos(4t), 5 sin(4t), 3t)...
Question 1. Let y : R -> R' be the parametrised curve 8 (t)= 1+ sin t Cost 5 Cos (a) (2 marks) Show that y is unit speed (7 marks) Find, at each point on the curve, the principal tangent T, principal normal (b) N, binormal B, curvature K, and torsion 7. (c) (3 marks) Show directly that T, N, B satisfy the Frenet-Serret frame equations (d) (3 marks) Show that the image of y lies in a plane...
1) For this problem use the following space curve: F(t) =< t, 3 sin(t), 3 cos(t) > a) Determine the unit tangent vector: T. b) Determine the unit normal vector: Ñ. c) Determine the curvature of this space curve at the point: (0,0,3). d) Determine the arc length of the curve between t = 0 and t = 1.
1) For this problem use the following space curve: r(t) =< t, 3 sin(t), 3 cos(t) > a) Determine the unit tangent vector: T. b) Determine the unit normal vector: Ñ. c) Determine the curvature of this space curve at the point: (0,0,3). d) Determine the arc length of the curve between t = 0 and t = 1.
1) For this problem use the following space curve: r(t) =< t, 3 sin(t), 3 cos(t) > a) Determine the unit tangent vector: T. b) Determine the unit normal vector: Ñ. c) Determine the curvature of this space curve at the point: (0,0,3). d) Determine the arc length of the curve between t = 0 and t = 1.
1) For this problem use the following space curve: Ft) =< 1,3 sin(t), 3 cos(t) > a) Determine the unit tangent vector: T. b) Determine the unit normal vector: N. c) Determine the curvature of this space curve at the point: (0,0,3). d) Determine the arc length of the curve between t O and t=1
12. Consider the curve given by ř(t) (3 cos(t),4t, 3 sin(t) (a) Which of the images below is the plot of the curve? IV 20 50 (a) Compute the arc length of the curve from t = 0 to t = 3. (b) Find the unit tangent vector T(t). (c) Compute the curvature of the curve at any value of t. 12. Consider the curve given by ř(t) (3 cos(t),4t, 3 sin(t) (a) Which of the images below is the...
A detailed explanation would be highly appreciated Question 2 25 (2.1) Consider the vector function C defined by r(t)-ti+2 j. (a) Find the unit tangent, the unit normal and binormal veetors T(t). N(t) and B(t) for C. (6) (b) Find an equation for the normal plane of C at the point (1, 2) (3) (c) Find an equation for the osculating cirele of Gat the turning point of C. (4) (2.2) Reparametrize the curve r(t) (e ,V2t , e) with...
a. Find the curvature of the curve r(t)- (9+3cos 4t)i-(6+sin 4t)j+10k. o. Find the unit tangent vector T and the principal normal vector N to the curve -π/2<t<π/2. r(t) = (4 + t)i-(8+In(sect))j-9k, Find the tangential and normal components of the acceleration for the curve r(t)-(t2-5)i + (21-3)j +3k. a. Find the curvature of the curve r(t)- (9+3cos 4t)i-(6+sin 4t)j+10k. o. Find the unit tangent vector T and the principal normal vector N to the curve -π/2