Find the point on the graph of z = 3x2 – 2y? at which vector n = (-12, –16, –2) is normal to the tangent plane. P =

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: Find the unit tangent vector at the indicated point of the vector function r(t)=e^(18t) cos t…

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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 unit tangent vector to the curve defined by T(t) = (- 3t, 5t, V100 t) at t = 7. T (7) =

A: The given vector is: r→(t)=-3t, 5t, 100-t2

Q: Sketch the graph of the plane curve . r(t) = ti − t3j and sketch the vectorsT(t) and N(t) at the…

A: Here we are taking the T(t) as the tangent vector and N(t) as the Normal vector Consider the…

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: Find the unit tangent vector and the length of the indicated portion of the curve: (a) r(t) = (6 sin…

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Q: Find the unit tangent vector for the parameterized curve: r(t) = 2ti + 2cos tj - 2 sint k

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Q: find the dot product of a vector function with itself. r(t) is a curve and the magnitude of r(t)=pi…

A: Let  u = a i^ +b j^ be a vector functionthe dot product of u with itself is given byu·u = a i^ +b…

Q: Find the unit tangent vector to the curve at the specified value of the parameter. r(t) = t³i +…

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Q: For the curve defined by r(t)=(; t³,;t²,t) calculate: The unit tangent vector, the unit normal…

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Q: nd the tangent plane to the equation z = a? – 4y? – 2y at the point ( – 3, 3, – 33)

A: In this question, concept of tangent  is used. Tangent A tangent is the line that runs parallel to…

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

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Q: I can't find the normal component of the acceleration. (aN)

A: For normal component of acceleration:

Q: What is the unit tangent vector to the curve r(t) =ť°j+tkwhen t = 2. Select one: 0 긁(2j + k) ㅇ…

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Q: Find the unit tangent vector to the curve at the specified value of the parameter. r(t) = t³i +…

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Q: Find the unit tangent vector and the parametric equation of the line tangent to the given curve at…

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Q: Find the equation of the tangent plane to z = e? + y + y? + 10 at the point (0, 5, 41). 2 =

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Q: Find the unit tangent vector T(t) at the point with the given value of the parameter t. 2t r(t) =…

A: In this question, we want to find the tangent unit vector of r(t) at t=0.

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: Find the unit tangent vector of the curve r(t) = (1 + 3 cos t)i + (3 sin t)j + t2k

A: Find the unit tangent vector of the curve.

Q: Find a parametrization of the tangent line at the point indicated. r(t) =〈t2, t4〉, t = −2

A: We have given equation of curve rt=t2,t4 a point on this line  r1=-22,-24=4,16 A vector parallel to…

Q: Find the unit tangent vector to the curve at the specified value of the parameter. r(t) = 6ti – t²j,…

A: To Determine: find the unit tangent vector to the curve at specified value of the parameter r(t)=6t…

Q: Find the unit tangent vector of the given curve. r(t) = 12t5i - 4t5j + 3t°k %3D

A: Given the vector function, r(t) , we call r′(t) the tangent vector provided it exists and provided…

Q: ). Determine the set Tp(Zf) of all tangent vectors to Zf at p. Is dim Tp(S) m ker d f.?

A: Sol

Q: Find the principal unit normal vector to the curve at the specified value of the parameter. r(t) =…

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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: Find the unit tangent vector T(t). r(t) = t²i + tj +4k, P(9, 3, 4) TO) (No Docpopcol

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Q: For the function f(x, y) = 2x² – 3xy + 8y² + 2x – 4y + 4, find a tangent vector to the level curve…

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Q: Find the equation of the tangent plane to z = e? + y + y² + 10 at the point (0, 5, 41). z =

A: Find equation of tangent plane from the given data

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: find the unit tangent vector to the curve at the specified value of the parameter.…

A: Therefore unit tangent vector of r(t→)=4cos(t)i^+4sin(t)j^  at t=π4 is  -12i^+12j^ Therefore the…

Q: Find the unit tangent vector T of the following curve: r(t)=(9-21)i+(21-4)j+(2+t)k

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Q: Find a tangent vector of unit length at the point with the given value of the parameter t. r(t) =…

A: Given, r(t)=(1+t2)i+t2j To find the unit tangent vector at the point t=1.

Q: For the function f(x, y) = 3x – 5xy + 4y – x + 4y – 2, find a unit tangent vector to the level curve…

A: Gradient of  function: Let z=f(x,y)z=f(x,y) be a function such that  partial derivating of with…

Q: Find the unit tangent vector for the curve C given by R(t) = cos³ ti + sin³ t j + 2k.

A: Note: - Since you have asked multiple questions, we will solve the first question for you. If you…

Q: find unit tangent vector of the given curve r(t)=(4-2t)i+(2t-3)j+(8+t^2)k

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Q: Find the unit tangent vector at the indicated point of the vector function r(t) = e3t cos fi+ et sin…

A: We use the following formula to find the unit tangent vector T(t)=V(t)/|V(t)|

Q: For the position vector R(1) = e'i+e²ª j, the velocity at t=ln3 is:

A: Consider the given position vector: R→t=eti+29e2tj Find Velocity vector: Differentiate w.r.t "t",…

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 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: a. Find the equation of osculating plane to Z1 at t=0

A: A(0) = < -2, 5, 4>     ---(1)  B(t) = < 3/5 cos t , 3/5 sin t , 4/5 >    => B(0)  =…

Q: Q4: Find the unit tangent and unit normal vector at t = 2 on the curve x = t? – 1, y = 4t – 3, z =…

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Q: Find the unit tangent vector to the curve at t r(t) = t°i + 3t?j, t= 2 T(2) =

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Q: The position vector in the xy plane is [t2,sin(t)].  What is the distance traveled by the particle…

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Q: Find the tangent plane to the equation z x? – 2y + 2y at the point (- 1, 5, – 39). z =

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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: Find the unit tangent vector T(t) at the point with the given value of the parameter t. r(t) = (2 -…

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Q: Find the tangent vector of r(t) = (t° , 3tª) at time t = 1. A) (3, 12) B) 15 C) (3, 7) D) 3t2 + 12t3

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Q: Let r(t)=r(t)=e¹i+e=¹j+tk. (a) Find the unit tangent, normal and binormal vectors T(t), N(t) and…

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