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Question 1. Let y : R -> R' be the parametrised curve 8 (t)= 1+ sin...
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...
2. Let (a, b) nonvanishing. Denote the Frenet frame by {T, N, B} vector a E R3 with R3 be smooth with = 1 and curvature...
2. Let (a, b) nonvanishing. Denote the Frenet frame by {T, N, B} vector a E R3 with R3 be smooth with = 1 and curvature k and torsion r, both Assume there exists a unit Ta constant = COS a. circular helix is an example of such curve a) Show that b) Show that N -a 0. c) Show that k/T =constant ttan a
2. Let (a, b) nonvanishing. Denote the Frenet frame by {T, N, B} vector a...
Find the curvature of the curve defined by F(t) = 227 + 5tj K= Evaluate the...
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 8 value 9p Show that the curve ที่(t-(2 + V2 cost, 1-sint, 3 + sin t , t e R lies at the...
I have no idea how to go about this question.
Question 8 value 9p Show that the curve ที่(t-(2 + V2 cost, 1-sint, 3 + sin t , t e R lies at the intersection of a sphere and a plane. Find the curvature at an arbitrary point on the curve.
Question 8 value 9p Show that the curve ที่(t-(2 + V2 cost, 1-sint, 3 + sin t , t e R lies at the intersection of a sphere and...
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...
X) 13.4.21 Find an equation for the circle of curvature of the curve r(t)-21 + sin(t) j at the point (z,1). (The curve...
X) 13.4.21 Find an equation for the circle of curvature of the curve r(t)-21 + sin(t) j at the point (z,1). (The curve parameterizes the graph of y = sin | 2x | in the xy-plane.) An equation for the circle of curvature is (Type an equation. Type an exact answer, using π as needed.)
X) 13.4.21 Find an equation for the circle of curvature of the curve r(t)-21 + sin(t) j at the point (z,1). (The curve parameterizes the...
1. A particle's position at time t is r(t) (t, 2et, e2t). Find the following in terms of t: nd the following in termns o (i) the distance traveled from the initial position at t0 (ii) the curvatu...
1. A particle's position at time t is r(t) (t, 2et, e2t). Find the following in terms of t: nd the following in termns o (i) the distance traveled from the initial position at t0 (ii) the curvature κ and torsion τ of the path (iii) the unit tangent, principal normal and binormal vectors T, N and B (iv) the tangential and normal components of the acceleration vector
1. A particle's position at time t is r(t) (t, 2et, e2t)....
find T,N,B curvature and torsion as a function of t for the space curve r(t)=sin t i+√2 cos t j+sin t k and find equation of normal and osculating planes
find T,N,B curvature and torsion as a function of t for the space curve r(t)=sin t i+√2 cos t j+sin t k and find equation of normal and osculating planes
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(sec...
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
(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...
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...
2. Let (a, b) nonvanishing. Denote the Frenet frame by {T, N, B} vector a E R3 with R3 be smooth with = 1 and curvature k and torsion r, both Assume there exists a unit Ta constant = COS a. circular helix is an example of such curve a) Show that b) Show that N -a 0. c) Show that k/T =constant ttan a
2. Let (a, b) nonvanishing. Denote the Frenet frame by {T, N, B} vector a...
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)...
I have no idea how to go about this question.
Question 8 value 9p Show that the curve ที่(t-(2 + V2 cost, 1-sint, 3 + sin t , t e R lies at the intersection of a sphere and a plane. Find the curvature at an arbitrary point on the curve.
Question 8 value 9p Show that the curve ที่(t-(2 + V2 cost, 1-sint, 3 + sin t , t e R lies at the intersection of a sphere and...
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...
X) 13.4.21 Find an equation for the circle of curvature of the curve r(t)-21 + sin(t) j at the point (z,1). (The curve parameterizes the graph of y = sin | 2x | in the xy-plane.) An equation for the circle of curvature is (Type an equation. Type an exact answer, using π as needed.)
X) 13.4.21 Find an equation for the circle of curvature of the curve r(t)-21 + sin(t) j at the point (z,1). (The curve parameterizes the...
1. A particle's position at time t is r(t) (t, 2et, e2t). Find the following in terms of t: nd the following in termns o (i) the distance traveled from the initial position at t0 (ii) the curvature κ and torsion τ of the path (iii) the unit tangent, principal normal and binormal vectors T, N and B (iv) the tangential and normal components of the acceleration vector
1. A particle's position at time t is r(t) (t, 2et, e2t)....
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
(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...
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