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Question 2 25 (2.1) Consider the vector function C...
Find the Unit Normal Vector and Unit Binormal Vector: ( 1 point) Consider the helix r(t)...
Find the Unit Normal Vector and Unit Binormal Vector:
( 1 point) Consider the helix r(t) (cos(8t), sin(8t),-3t). Compute, at- A, The unit tangent vector T-〈10.8 10884854070| , -0.46816458878| B. The unit normal vector N 〈 C. The unit binormal vector B-〈 1 ǐ ,1-0.35 11 23441 58 0
The curvature of vector-valued functions theoretical Someone, please help! 2. The curvature of a vector-valued function r(t) is given by n(t) r (t) (a) If a circle of radius a is given by r(t) (a cos...
The curvature of vector-valued functions theoretical
Someone, please help!
2. The curvature of a vector-valued function r(t) is given by n(t) r (t) (a) If a circle of radius a is given by r(t) (a cos t, a sin t), show that the curvature is n(t) = (b) Recall that the tangent line to a curve at a point can be thought of as the best approx- imation of the curve by a line at that point. Similarly, we can...
8. Find the length of the curve given by F(t)=(3 sin(21),19,3cos(21), for ISIS 3, rounded to...
8. Find the length of the curve given by F(t)=(3 sin(21),19,3cos(21), for ISIS 3, rounded to the nearest tenth. (6 points) 9. Suppose that a space curve given by the vector function () = (21'.1'. 36). a. Find parametric equations for the tangent line to this space curve at the point where - (4 points) b. Find the unit tangent vector, the unit normal vector, the unit binormal vector and the curvature for this space curve at the point where...
(1 point) Consider the helix r(t)-(cos(-4t), sin (-4t), 4t). Compute, at t A. The unit tangent vector T-( B. The unit normal vector N -( C. The unit binormal vector B( D. The curvature K = Note that...
(1 point) Consider the helix r(t)-(cos(-4t), sin (-4t), 4t). Compute, at t A. The unit tangent vector T-( B. The unit normal vector N -( C. The unit binormal vector B( D. The curvature K = Note that all of your answers should be numbers
(1 point) Consider the helix r(t)-(cos(-4t), sin (-4t), 4t). Compute, at t A. The unit tangent vector T-( B. The unit normal vector N -( C. The unit binormal vector B( D. The curvature K...
2. Consider the circular helix r(t)- (a cos t, a sin t, bt) where a > 0,b > 0. Let P(0, a, T) be ...
please answer all the 4 parts
of this question
2. Consider the circular helix r(t)- (a cos t, a sin t, bt) where a > 0,b > 0. Let P(0, a, T) be a point on the helix (a) Find the Frenet frame (T, N, B) at the point P (b) Find equations for the tangent and normal line at P (c) Find equations for the normal plane and the osculating plane at P (d) What is the curvature at...
Find the derivative, r'(t), of the vector function. r(t) = eti- j+ln(1 + 7t)k r'(t) =...
Find the derivative, r'(t), of the vector function. r(t) = eti- j+ln(1 + 7t)k r'(t) = Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. T = 5e, y = te, c = tetp:/5, 0, 0) x(t), y(t), z(t) =
Question 1. Let y : R -> R' be the parametrised curve 8 (t)= 1+ sin...
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...
For the following equations : x= 2t^2 , y = 3t^2 , z= 4t^2 ; 1 <=t <=3 A) write the position vector and tangent ve...
For the following equations : x= 2t^2 , y = 3t^2 , z= 4t^2 ; 1 <=t <=3 A) write the position vector and tangent vector for the curve with the parametric equations above B) Find the length function s (t) for the curve C) write the position vector as a function of s and verify by differentiation that this position vector in terms of s is a unit tangent to the curve.
1. a. Consider the curve defined by the following parametric equations: r(t) = et-e-t, y(t) = et ...
1. a. Consider the curve defined by the following parametric equations: r(t) = et-e-t, y(t) = et + e-t where t can be any number. Determine where the particle describing the curve is when tIn(3) In(2). 0, ln(2) and In(3). Split up the work among your group Onex, vou l'ave found i lose live polnia, try to n"惱; wbai ille wlu le curve "u"ht lex k like. b. Verify that every point on the curve from the previous problem solves...
7) Consider the surface S: x2 +y2 - z2 = 25 a) Find the equations of...
7) Consider the surface S: x2 +y2 - z2 = 25 a) Find the equations of the tangent plane and the normal line to s at the point P(5,5,5) Write the plane equation of the plane in the form ax + By + y2 + 8 = 0 and give both the parametric equation and the symmetric equation of the normal line. b) Is there another point on the surface S where the tangent plane is parallel to the tangent...
Find the Unit Normal Vector and Unit Binormal Vector:
( 1 point) Consider the helix r(t) (cos(8t), sin(8t),-3t). Compute, at- A, The unit tangent vector T-〈10.8 10884854070| , -0.46816458878| B. The unit normal vector N 〈 C. The unit binormal vector B-〈 1 ǐ ,1-0.35 11 23441 58 0
The curvature of vector-valued functions theoretical
Someone, please help!
2. The curvature of a vector-valued function r(t) is given by n(t) r (t) (a) If a circle of radius a is given by r(t) (a cos t, a sin t), show that the curvature is n(t) = (b) Recall that the tangent line to a curve at a point can be thought of as the best approx- imation of the curve by a line at that point. Similarly, we can...
8. Find the length of the curve given by F(t)=(3 sin(21),19,3cos(21), for ISIS 3, rounded to the nearest tenth. (6 points) 9. Suppose that a space curve given by the vector function () = (21'.1'. 36). a. Find parametric equations for the tangent line to this space curve at the point where - (4 points) b. Find the unit tangent vector, the unit normal vector, the unit binormal vector and the curvature for this space curve at the point where...
(1 point) Consider the helix r(t)-(cos(-4t), sin (-4t), 4t). Compute, at t A. The unit tangent vector T-( B. The unit normal vector N -( C. The unit binormal vector B( D. The curvature K = Note that all of your answers should be numbers
(1 point) Consider the helix r(t)-(cos(-4t), sin (-4t), 4t). Compute, at t A. The unit tangent vector T-( B. The unit normal vector N -( C. The unit binormal vector B( D. The curvature K...
please answer all the 4 parts
of this question
2. Consider the circular helix r(t)- (a cos t, a sin t, bt) where a > 0,b > 0. Let P(0, a, T) be a point on the helix (a) Find the Frenet frame (T, N, B) at the point P (b) Find equations for the tangent and normal line at P (c) Find equations for the normal plane and the osculating plane at P (d) What is the curvature at...
Find the derivative, r'(t), of the vector function. r(t) = eti- j+ln(1 + 7t)k r'(t) = Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. T = 5e, y = te, c = tetp:/5, 0, 0) x(t), y(t), z(t) =
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. a. Consider the curve defined by the following parametric equations: r(t) = et-e-t, y(t) = et + e-t where t can be any number. Determine where the particle describing the curve is when tIn(3) In(2). 0, ln(2) and In(3). Split up the work among your group Onex, vou l'ave found i lose live polnia, try to n"惱; wbai ille wlu le curve "u"ht lex k like. b. Verify that every point on the curve from the previous problem solves...
7) Consider the surface S: x2 +y2 - z2 = 25 a) Find the equations of the tangent plane and the normal line to s at the point P(5,5,5) Write the plane equation of the plane in the form ax + By + y2 + 8 = 0 and give both the parametric equation and the symmetric equation of the normal line. b) Is there another point on the surface S where the tangent plane is parallel to the tangent...
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