For the space curve in R° graphed below, which vector would be the unit normal vector at time t-1? You can assume each is of length one, and the curve is "living" on the screen, i.e., it is flat.

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 &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: Sketch the curve of the vector function r(t) = 3ti+ (3t + 1)j,-1<ts2, and indicate the orientation…

A: The given curve in vector form: r(t)=3ti+(3t+1)j The point of t is -1≤t≤2 To find the curve at the…

Q: Calculate the velocity and acceleration vectors and the speed at the time indicated in the figure…

A: Solution:Givenr(s)=11+s2,s1+s2    s=2To find velocity,acceleration and the speed

Q: Find the velocity and acceleration vectors in terms of u, and ue en r=6 sin t and 0= 9t

A: The velocity is given by            v = r' ur +rθ' uθandThe accerleration is given by        a =r"-r…

Q: Given a curve Determine the unit tangent vector, T, the principal unit normal vector, N and the…

A: A

Q: find T, N, and B for the curve at the indicated point. Hint: After finding T', plug in the specific…

A: The unit tangent vector T, the unit normal vector N and the unit binormal vector B are three…

Q: H.W. Find the unit normal vector to the curve at t=2, r(t) = 4t i-3 t j.

A: Unit normal vector is N(t)=T'(t)‖T'(t)‖ here T(t) is unit tangent vector and T(t)=r'(t)‖r'(t)‖ So we…

Q: Find the principle unit normal vector to the curve given below at the specified point. r(t) =…

A: According to question given thatr(t)=ti+6t2j, t=3

Q: If is a smooth curve given by a vector function r(t) a &lt; t &lt; b and is a constant vector, show…

A: So we have;

Q: Find the Unit normal VEctor N to rCt) at 1777 ン 4 N (t)= 0

A: From the given data

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

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Q: Determine whether the following trajectory lies on either a circle in R or a sphere in R° centered…

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Q: Find the unit tangent vector T, the principal unit normal vector N, and the unit binormal vector B…

A: Consider the curve     Ct: rt =cost,sint,t (i) unit tangent vector                  The unit tangent…

Q: Fix a point P on the line ( and let N be normal unit vector to (. Show 5. (. that if N' is another…

A: Given: A fixed point P on the line l. An unit vector N normal to l.   To show: If N' is another unit…

Q: Given the vector function 7(t) = (t +3, 7t – 5) %3D Calculates the principal normal vector (t)when t…

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Q: the unit tangent vector of a(t)=

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Q: Consider the following vector function. 1, 12², 1²) (a) Find the unit tangent and unit normal…

A: The given vector function rt=3t, 12t2, t2

Q: Suppose that you drawa point x in the middle of a page, and a curve going through X in such a way…

A: Given: Suppose that you draw a point x in the middle of a page, and a curve going through X in such…

Q: Find the point on the graph of z = 3x2 – 2y? at which vector n = (-12, –16, –2) is normal to the…

A: Shown below

Q: For the space curve in R° graphed below, which you can assume is laying flat on the screen, at time…

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Q: Given the vector function. Calculates the principal normal vector N(t) when t=6.9

A: Question- Given the vector function. Calculates the principal normal vector N(t) when t=6.9 ?

Q: Given the vector function 7(1)=(31²-1, 1-8√F³, 12t-4), find the speed & arc length of the curve on…

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Q: The graph of the vector function r(t) = ti +t²j+2k is

A: Graph of vector function  r(t) is :  r(t)= t i + t2 j + 2k

Q: 6. d(X, {) seems to depend on the choice of P on { and on the unit normal vector N. Show that if N'…

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Q: Write formulas for the unit normal and binormal vectors of a smooth space curve r(t)

A: The formulas for unit normal vector  and binomial vectors of a smooth space curve r(t).

Q: The unit tangent vector of 7(t) = ti – j- tk at t = 1 is Select one: O A. i O B. -- k OC. i+ j- O D.…

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Q: If the position vector r(t)=e9t i +9sqrt(2)t j + e-9t k, compute the normal component of the…

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Q: Question « Which of the following is a normal vector to the plane which is normal to the curve r(t)…

A: This is a problem from vector calculus.

Q: Find the principal unit normal vector N for the curve r(t). r(t) = (3 + t)i + (7 + In(cos t))k, -1/2…

A: Given, r(t)=(3+t)i+(7+ln(cost))k Let r(t) be the differentiable vector-valued function and let T(t)…

Q: The unit tanaent vector T and the principal unit normal vector N for the parameterzed curve 214)3D…

A: Binormal vector , B(t) = T×N Torsion for r→(t) = N'(t).B(t)

Q: Find the principle unit normal vector to the curve given below at the specified point. r(t) = ti +…

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Q: Consider the following graph. (4,5) 2 (1, 2) 3 (a) Find the component form of the vector v. (b)…

A: Given vector is as shown below :

Q: Find the point on the graph of z = 3x2 + u? at which vector n (24, 2, –1) is normal to the tangent…

A: Gradient of the surface denote the normal direction.

Q: The divergence of a vector D for rectangular coordinate is equal to [1/p / dp (pDp)] + [1/p Dø/dø]+…

A: We have to find divergence in rectangular coordinate

Q: The graph of the vector functionr (t) = 2i +tj+tk is

A: 3d graph related problem.....

Q: If the position vector of a particle P is r(r) (3cos t,5sin7,4 cos t) a) Show that the speed of the…

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Q: Compute the unit binormal vector B for the following parameterized curve: F(t) 4 2 3t, 1

A: Given:    r(t) = ⟨ t2/2 , 4-3t , 1 ⟩

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: Consider the curve F(1)=i +(/2 In(?))j + 1 -k. | а) Find the binormal vector B(1)

A: Given the curve  r→(t) = i→ + 2ln(t)j→ + 1tk→

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

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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: 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: The position vector of a particle in space is given as R = (1.25 t2) i+ (t)j Find the Normal vector…

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Q: r(t) = (t³,6t), t≥0

A: Given curve r→(t)=t3,6t,t≥0 The objective is to calculate principle unit normal vector. First…

Q: Sketch the curve of the vector function r(f) = ti +4costj, and indicate the orientation of the…

A: We have to sketch the curve of the vector function rt=ti+4costj, and to indicate the orientation of…