If r(t) = < In t, ecost, t2 >, then unit tangent is a principal unit normal is a and its curvature is a vector scalar

Q: find a unit normal vector UN to the curve y = x at the point p(1,3)?

A: The given curve is y = x3, we can write it as x3 - y = 0 = f(x,y,z), where z = 0

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

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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: find a vector normal to the plane with the given equation. x − z = 0

A: Given: Plane: x-z=0 To Find: A vector normal to the given plane

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

A: Given ,

Q: Find the radius of curvature of y=xª at (1,1).

A: Here we have to find the radius of the curvature of y=x4 at (1,1)

Q: Find an equation of the tangent plane and a normal line to the surface z = In Vx2 + y2 at the point…

A: Given that: z=lnx2+y2

Q: /Find the tangent and normal vector for curve r= (5sin n i+5 cos n j+n k) n=(In 2t)

A:

Q: Find the extreme values of the function z= &r+2ry-3r+y+1 and show that only one of the two extrema…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 1) Calculate the curvature of the position vector r(t) = sin tāx + 2costāy + V3 sin tāz is a circle,…

A:

Q: A particle moving along the curve (t) = (cost+t sint)i + (sint - cost)j,find acceleration components…

A: For any curve r(t)  Component of acceleration can be given by  Tangential component aT= v'(t) =…

Q: TU? TU? r(t) = (/ * du, sin -du ) , t > 0 COS 2 2

A: r(t)=∫0tcosπu22du,∫0tsinπu22du,t&gt;0 We have to find the unit tangent vector T and Curvature K for…

Q: Find the curvature of the curve C: r (t) = (e, e', 2t) at t = 0

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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…

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Q: Consider the vector function given below. r(t) = (13t, 2 cos(t), 2 sin(t))

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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: Find the unit tangent vector to r(t) =〈sin t,t, cost〉at t = π.

A: rt=sin t, t , cos t at t=π

Q: b.) show that brnormal of the muolute the unit *-ズ+(c-s)で g =dG) |k-s) K| K* where K is the…

A:

Q: 1) Calculate the curvature of the position vector r(t) = sintāx + 2costāy + V3 sin t āz is a circle,…

A: Given position vector is  r→t=sintax→+2costay→+3sintaz→ Then unit tangent vector is…

Q: use Eq. (3) to calculate the curvature function κ(t)  r(t) = (t−1, 1, t)

A: Solution:Given     r(t)=(t-1, 1,t)To find κ(t):κ(t)=r'(t)×r''(t)r'(t)3

Q: for the follawing , find the unit tangent vector: parameterized curve rit) =<2 sint) , 2 cos lt),5…

A: Given: r(t)=2sin(t),  2cos(t), 5cos(t),  0≤t≤π The unit tangent vector to curve r(t) is…

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: The curvature of y =x is

A: In this question we have to find the curvature of the given function which we can find out by using…

Q: Find a unit tangent vector to any point on the curve x = a cos wi, y = a sin wt, z = bt where a,b,w…

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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: A normal vector to the tangent plane for the surface a y"z* = 1 at the point (1, 1, –1) is: %3D…

A:

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: Show that if r(t) is perpendicular to the tangent vector r′(t) for all t, then the curve r(t) lies…

A: If r(t) is perpendicular to the tangent vector r′(t) for all t, then the curve r(t) lies on a sphere…

Q: Let r(t) = (sin t-t cos t)i + 7j+ (cos t+t sin t) k . Find the following: (a) Unit tangent vector T…

A:

Q: Find the curvature of the cardioid r=a(1+cosθ) at θ=0.

A: Given equation of cardioid is Derivatives of polar curve are

Q: Consider the Vector function a.) Find the もこ0 arc leng th of rlt) from to b.) Find the curvature a…

A: The given vector function is rt=t,t2,23t3. a) Find the arc length of rt from t=0  to  t=1 as…

Q: Find the unit tangent vector T(t) and the unit normal vector N(t) and the curvature K for r(t) = (t,…

A: Consider the given vector, rt=t,3cost,3sint Find the derivative with respect to t.…

Q: 1) Calculate the curvature of the position vector ŕ(t) = sin t āx+ %3D 2costay + v3 sin t āz is a…

A: To calculate the curvature of the position vector r¯t=sintax¯+2costay¯+3sintaz¯  is a cirlceAlso to…

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: he normal vector to the tangent plane for the surface point (1, 2, -1) is: Select one: None of them…

A: topic:- application of derivatives

Q: Write the equations of the tangent plane and the normal line to the surface y + In(xz) Z = at the…

A: I have appended the formula used in the solution part

Q: Find equations for (a) the tangent plane and (b) normal line at the point P, on the given surface 1)…

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

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Q: Show that for a plane curve the torsion T = 0.

A: We have to shown that, For a plane curve the torsion T=0

Q: ; Consider the vector function r(t) = ti + t²j+t°k. Compute the curvature of r at time t = 2.

A: Hello. Since you have posted multiple questions and not specified which question needs to be solved,…

Q: ind a formula for a vector normal to the plane tangent to f(x,y) at (xo, Yo).

A:

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

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Q: Find an equation of the tangent plane to the surface z = xy at (1,2,2).

A: The given surface can be written as F(x, y, z)=0, where F(x, y, z)=xy-z

Q: A curve C is defined as the intersection of the surfaces x^2+y^2=2 and z=x^2 . Find the curvature of…

A: We are given 2 surfaces in the 3D (three - dimension). We will use the definition of the curvature…

Q: Find the gaussian and mean curvature functions of the surface m given by the equation y3=y1y2 in R³…

A: First parameterized the equation.

Q: find equations for the(a) tangent plane and(b) normal line at the point P0 on the given surface. x2…

A: GivenSurface F(x,y,z)=x2+y2+z2-3=0Point of…

Q: The curvature of y = x2

A: so we have to find curvature of y =  x2. we use the formulae for curvature  k(x) =…