'. Given r(t)= (cos 21, sin 21, 31). Find the normal vector N(t), and explain. Then find the equation of the normal plane at the point P(-1,0,37/2).

Q: Find an equation of the normal line to the parametric surface given by R(u, v) = ((2+ cos v) cos TU,…

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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: Find the principal unit normal vector N of the curve: r(t)=(7tsint+7cost)i+(7tcost-7sint)k

A: The given curve is r→t=7tsint+7costi^+7tcost-7sintk^ We have to find the principal unit normal…

Q: Q1/Find the tangent and normal vector for curve = (5sin n i+5 cos n j+n k)

A: we have to find the tangent and normal vactor

Q: r(t) = (sin 7t, t, cos t)

A: The vector equation is r(t)=sinπt, t, cosπt. Here, x=sinπt, y=t, z=cosπt Then x=sinπy, and z=cosπy…

Q: Q1) Find the tangent &normal vector for the curve r-asint?i+acos tj +bt?k

A: Given that The position vector is r→=a sin t2i→+a cos t2j→+bt2k→   The tangentT→ vector is given by…

Q: Find the tangent, normal, and binormal vector functions for the following three curves:   curve 1:…

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Q: Find a vector normal to the plane with the given equation. 3(x – 5) – 5(y – 1) + 10z = 0 n =

A: Consider the equation of the plane passing through a general point Po and with normal vector n.

Q: 4.a. Find the unit tangent and normal vectors to r(t) = 4 cost i + sin t j at t = /2. Sketch a…

A: Given that rt=4cost i +sin t j Then r't=-4sin t i  +cos t. The formula for tangent vector is…

Q: Find the principal unit normal vector r(t) = cos 3ti + 2 sin 3tj + k to the curve at the specified…

A: To find the principal unit normal vector of r(t)=cos 3t i + 2 sin 3t j+k with t=π first…

Q: Show that at every point on the curve r (t) = ⟨et cos t, et sin t, et⟩ the angle between the unit…

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Q: The principal unit normal vector on the curve r(t)= (2 sint,2cost) %3D (a) always points directly…

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Q: Sketch the curve parametrized by r(f) = (1 – 12, 1) for -1sı<1. Compute the tangent vector at i = 1…

A: Let's first draw the curve -  Domain - -1 ≤ t ≤ 1 where, we can take values of t as -  t = -1, -0.5,…

Q: Q1/Find the tangent and normal vector for curve (5sin n i+5 cos n j+n k)

A: We have given r(t) and we have to find tangent and normal vector to r(t)

Q: find the curve’s unit tangent vector. Also, find thelength of the indicated portion of the curve. .…

A: Given:                  rt=cos3tj+sin3tk,     0≤t≤π2                 v=ddtrt=ddtcos3t j+sin3t…

Q: Sketch the curve represented by the vector-valued function                               r(t) = 2…

A: Given information: Vector-valued function rt=2costi+tj+2sintk trigonometric identity, sin2t+cos2t=1…

Q: For the curve given by the vvf r(t) = ti + 2t²j+t³k, find the unit tangent T(t), principal normal…

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

Q: Find equations of (a) the tangent plane and (b) the normal line to the surface 2(x−2)^2 + (y−1)^2 +…

A: Given surface is Firstly, we find all first order partial derivatives At point (3,3,5)

Q: Consider an object moving according to the function from position r(t) = acoswt i + asenwt j. To…

A: As per the question we have to find the tangential and normal vector components of the path defined…

Q: At the Find the moments when the two distance, given vectors of velocity and acceleration are…

A: The given vector is R→t=2 i^+5 cost j^+3 sint k^ ,   0≤t≤π ....(1) To find: the moments of the…

Q: The normal component of the acceleration vector for an object with position vector r(t) = (cos(t),…

A: To check the given statement for True/False.The normal component of the acceleration vector for an…

Q: A particle is moving along the curve whose position vector is given: R(t) = (cost + tsint)i + %3D…

A: R(t)→=cost+t sinti+sint-t costj+4kFind the unit normal vectorSome…

Q: a)What is the slope of the tangent line to the curve y=2sin4x  at x=⊼(pie)/4? b) Find a unit vector…

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Q: Find the length of the curve with the given vector equation. r(t) = cos ti+ sin tj+ 3t k; 0sts3

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Q: Find the equations of (i) the tangent plane and (ii) the normal line to the surface z = excos(y) at…

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Q: A particle is moving along the curve whose position vector is given: R(t) = (cost + tsint)i + (sint…

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Q: Determine a direction derived from the point P and in the direction of the versor vector → informed…

A: Given:  Let f be a differentiable function at the point (a, b). Then f has a directional derivative…

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: Find equations of the following. 2(x – 7)2 + (y – 5)² + (z – 6)² = 10, (8, 7, 8) %3D - (a) the…

A: Suppose we have given a surface .Then; The equation of tangent plane at   is  . The equation…

Q: Find the Tangent vector, the Normal vector, and the Binormal vector (T, N and B) for the curve r(t)…

A: This question can be solved using the concept of vectors and derivatives.

Q: The unit normal vector N to the curve 7(1) = (1, t, at t=0 is

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Q: Q1:(A) What is the angle between the normal vectors to the curve F (1) = (2x² + x + 1)i + (+1)j +rk…

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Q: Find the Tangent vector, the Normal vector, and the Binormal vector (T, N and B) for the curve = (3…

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Q: Let P be the point (2, -1, 2) and Ø,: x² + y² – z² = 10. (i) Find the unit normal vector to the…

A: (c) The given surface is ∅1: x2+y2-z2=10 and the point P: 2,-1,2. (i) The unit normal vector to the…

Q: 3x2 – 4y2 at which the vector 11. Find the points on the graph of z = (3, 2, 2) is normal to the…

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Q: For the curve attached, how do I get the  1) unit tangent vector 2) the unit normal vector  3)…

A: Solution :-

Q: 1. Given the following lines: 3x D:: * = y – 1 Dz: x+ y-6 = 0 a-) Give a normal vector associated…

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Q: Find the position vector for the particle with acceleration, initial velocity, and initial postion…

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Q: Q1) Find equation of plane normal to vector 3i + 2j – k and pass through point (1,1,5).

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Q: Find the unit tangent , nomaand binormaL vectors 2. 2-Ycet [csti * sint j + x].

A: As per the guidelines, we are supposed to answer only one question at once. Kindly repost the other…

Q: Find the principal unit normal vector for the helix r(t) = 2 cos ti + 2 sin tj + tk.

A: Given, r(t)=2 cost i+2 sint j+t k

Q: Find the principal unit normal vector N for the curve r(t). (1) = (1² + 3) +(2t – 8) k". %3D

A: Given: r(t)=(t2+3)j+(2t-8)k.

Q: Find the unit tangent, normal and binormal vectors T, N and B for the curve at the point (0, 7, -1).

A: The curve is defined by the vector function rt=sint2,t2,cost2 on the domain [0,∞) To find the unit…

Q: K has equation G(x, y) = 0, and G is differentiable and G and G,y are bo e point P (a, b) on K, then…

A: In this question we will use basic of calculus i.e concept of vector calculus. We will use concept…

Q: A tangent vector to the curve Cat P corresponds to: A) 7 = (1,–1, –v2)

A: Given that                   C is an intersection curve in the first octant, between the surfaces S1…

Q: 2. Let C be a curve given by r(t) = (e' sin t, e' cos t, /2e'), t is real. (a) Find the binormal…

A: Given, r(t)=etsin t, etcos t,2et

Q: B- Find the length of the curve given by the position vector r=, =r'i+(1+(1/3)x')j+(1-(1/3)')k for

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Q: Find the unit tangent vector to the curve r(t) = (2sin(t),2cos(t)) at the points t =-n, t=0 and t…

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Q: Sketch the curve with the vector equation ř(t) = (sin t, t). Indicate with an arrow the direction in…

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