Let 3 : (3t, r = be a curve in 3-dimensional space having unit tangent and normal vectors u and . Find the curvature of this curve.

Q: For any curve in the plane, the curvature is the absolute value of the geodesic curvature. * True…

A: As per our guidelines we are supposed to solve only one question. For the solution of the first…

Q: Find the curvature of r(t) = at t = ,.

A: Given: r→t=3cost, 3sint, t Calculation: Compute the Curvature at t=π2 as follows. It is known that…

Q: Let r= (3v/2t, 3ť, /2t³) be a curve in 3-dimensional space having unit tangent and normal vectors u…

A:

Q: Express the curvature of a twice-differentiable curve r = ƒ(u) in the polar coordinate plane in…

A:

Q: Find the curvature and radius of curvature of the plane curve at the given value of x. y = xn, x =…

A: Given ,

Q: Q1. Find the curvature of the line whose parametric equations are given as: x = -2+t, y =3+ 2t, z…

A:

Q: 2.Let a be a unit speed curve lying on a sphere center c and radius a > 0. Find the minimum value of…

A: Given That : Let α be the unit speed  curve lying on a sphere center c and radius a>0. To Find :…

Q: 3. Find the curvature of the plane curve (t, t") at t = 1.

A: see below the answer and calculation as per bertleby guideline I have to solve only 1 question. For…

Q: Calculate the curvature function for r

A:

Q: 8) If curvature of a space curve at (2,3) is 8 and curvature at (7,1) t=7 is 1, what can be said…

A: ANSWER:

Q: Let P be a point on a regular surface S and let f and g be two curves on S passing through P and…

A:

Q: a) Find a plane curve whose signed curvature is given by k,(s) where a is a positive constant and s>…

A: The given signed curvature is ks(s)=12as

Q: Find curvature of the parametric curve r(t) = (t, t3 – t, 3) at t = 1. Show your work.

A:

Q: A curve is given in polar coordinate as r=R(f). What is its curvature? Find it in terms of R,R' and…

A:

Q: If a curve has the property that the position vector r(t) is always perpendicular to the tangent…

A: given that, a curve has the property that the position vector r(t) is always perpendicular to the…

Q: Find the center of curvature of the curve y at (0, 1). (A) (0, 2) B) (1, 1) c) (0, 3) D) (0,0)

A:

Q: Let R be a vector function whose graph is smooth curve such that, R(2) =, R'(2) = , and R"(2) =…

A: Radius of curvature of teh function is given by formula, R = (1+y'(x)2)32y''(x)

Q: Consider the following curve 7(1) = (-2sin(e), –V5,2cos() (a) Find the unit tangent vector. (b) Find…

A: The formula to obtain the unit tangent vector for any curve r(t) is given by: The formula to find…

Q: If r(t) = , then unit tangent is a principal unit normal is a and its curvature is a vector scalar

A: Explained below

Q: |x'y" -y': y'a - y'= es K(t) = (x2 + у'?

A:

Q: Use the curvature formula to find the following parameterized curve

A: Solution: The objective is to find the curvature

Q: 2-Show that the regular curve a = a(s) is a straight line if and only if its curvature k is…

A: Here we have to show that a regular curve is a straight line if and only if, its curvature is…

Q: Find the currvature and radius of curvature of the plane curve at the given value of x. y%3D 5x+ 7.…

A:

Q: A particle is moving in space with position function R(t) = (cos(4t), sin(4t),5 – 3t) Find the…

A:

Q: Show that curvature at an inflection point of a plane curve y = f (x) is zero.

A: We have to show that curvature at an inflection point of a plane curve y=fx is zero. We know that if…

Q: A curve has a vector equation r = ti+ 4 sin(t)j + 4 cos(t)k. Find the curvature, K.

A:

Q: Find the curvature for the following vector function. 1. r(t)=( 4t, -t², 2t³)

A:

Q: Find the center of curvature of y = x3 at the point (1, 1) A. (-4, 8/3) C. (6, -2/3) B. (4, -8/3)…

A:

Q: Compute the mean curvature for u = 1 and v= 0.

A: Given,           X(u, v)=u2-cosv, u+sin t, cosv To find the mean curvature for u=1, and v=0.

Q: Find the curvature of r(t) = at the point (1,0,0)

A:

Q: Find the center of curvature of the curve y=Inx at (1, 0). A) (4, 3) (в) (3,4) c) (3, -2) D (-2, 3)

A: Ans D

Q: Find the curvature of the curve given by r(t)=(4sint, 4, 4cost)

A: Given that : r(t)=4sint, 4, 4cost Therefore, r'(t)⇀=4cost, 0, -4sint. Therefore,…

Q: 2. Show that if a : [a, b] → R" is a regular parameterization of a curve then the curvature at α(t)…

A: Let,  is a regular parameterization of a curve To show the curvature at  is

Q: 7.) rCt) = (5+,3cot), 3sind), 7.1-> Find the arc length of the curve. 72-) Find the unit tangent and…

A: as per our company guidelines we are supposed to answer ?️only first 3️⃣ sub-parts. Kindly repost…

Q: Find the curvature of the curve. r(t) =<2t, - 3sin t, 3cost)

A:

Q: Find k (curvature) and t (torsion) for curve C represented by F(t)=(e^t,-e^t,(2t)^1/2)

A:

Q: Show that if M" has constant sectional curvature C then Ricci and scalar curvature of M" are Ric =…

A: We know that from given data: If M has a constant sectional curvature C , k. The Uniqueness of this…

Q: Let r (t,t,t) be a curve in 3-dimensional space having unit tangent and norma V2 vectors u and n.…

A: We will use formula of curvature of a curve to solve it.

Q: Find the curvature of the vector-valued function. r(t) = (e3t,e)

A:

Q: Given the parametric equation of a planar curve r(0) e C² , derive the following equation: dn dr =-k…

A: Given, The parametric equation of a planar curve rθ∈C2. To derive- dndθ=-kdrdθ where ndenotes the…

Q: #3. Use the cross product formula to calculate the curvature of the following vector function. r(t)…

A:

Q: 1) Calculate the curvature of the position vector F(t) = sin t ax+ 2cos tay + V3 sin tāz is a…

A:

Q: 8) If curvature of a space curve at (2,3) is 8 and curvature at (7,1) t=7 is 1, what can be said…

A: Given that curvature of a space curve at 2,3 is 8 and curvature at 7,1 is 1.

Q: Example: Find the curvature of the curve, where a&b> o r= (acos ti + asintj+ btk)

A:

Q: What is the radius of curvature of the polar curve r = 02 at 0=3/2?

A:

Q: 1) Calculate the curvature of the position vector 7(t) = sin tax + %3D 2cos tay + V3 sin tāz is a…

A: In this question we have to find curvature and radius of curvature.

Q: Find the curvature of the curve r(@) = 3Sinwî + 3Cosq ĵ + 3wCotwk %3D

A: We find the curvature with standard formula.