4. Consider the vector function v(t) = (t, t², t³). (a) (10 points) Find the unit tangent vector function T(t), the unit normal vector function N(t), and the binormal vector function B(t). (b) (5 points) Give an equation for the normal plane to v in terms of t. (c) (10 points) Find the curvature к and the torsion 7 in terms of t.

Q: 5) Given: r(t) =( 2t, t2, ) O Find parametric equations for the tangent line to the curve at t O…

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Q: Let F(t) = (1, ²,4) and P = (2, 10, 4). Consider the curve C parametrized by F(t). Compute a tangent…

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Q: EXERCISES 5: Find equations for the (a) tangent plane and (b) normal line at the point Po on the…

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Q: 4. Let r(f) = ° 13 i - 6fj + Pk. (a) Find the unit tangent vector T(t) and T(3). | (b) Find the…

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Q: Find the Unit Tangent (T (t)) b. Unit Normal Vectors (N(t)) c. Find Curvature (k (t)) & (k (3),t=3)…

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Q: For the given position vectors r(t) compute the unit tangent vector T(t) for the given value of t.…

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Q: Find the unit tangent vector of the given curve. r(t) = (7t cost-7 sin t)j + (7t sin t + 7 cost) k…

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Q: What is the unit tangent vector to the curve r(t)=⟨cost, sint, et⟩ at the point where t=0?

A: Given:          r(t)=cost,sint,et at t=0           r→(0)=cos(0),sin(0),e0          r→(0)=1,0,1…

Q: Calculate the curvature and torsion for the following trajectories given by x(t) x(t) x + y(t)ý +…

A: Since you have asked multiple questions, we will solve the Question (iii) for you. If you want any…

Q: 3. (a) Given the vector valued function r(t) = 4cos nti + 4 sin ntj + tk. Find the position vector,…

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Q: Given r(t)=2e²i+(2e“ cost)j+(2e" sint)k . (a) Find the tangent vector, T(t) and the normal vector,…

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Q: -T, N. de (i) The concept of curvature and radius of curvature are defined by extending those con-…

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Q: Consider the following vector function. - (46, ½-12², 1²) r(t): (a) Find the unit tangent and unit…

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Q: Given the parametric curve r (t)=⟨sin(πt),t⟩ where −1≤t≤1, find r ′ (t) and sketch the curve,…

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Q: Given the curve f (t)= (2t2 - 3, 3 - t, 3 + 2t?). Find the equation of the line parallel to the…

A: Consider the equation as shown below: Here, curve ft =2t2-3, 3-t, 3+2t2 Here, the object is to find…

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: b) For a general curve r: 1R, define the vectors t(s), n(s) and b(s) as t(s) - r(s) (s) and b(s) =…

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Q: Calculate the curvature and torsion for the following trajectories given by x(t) x(t) x + y(t) ŷ +…

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Q: For 1=1, the point Plies on the curve given by the parametric equations +3 -8 1+1 1+1 Calculate,…

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Q: 4. for the vector function 7(t) = t³i+t?j a) Find the velocity, acceleration and unit tangent vector…

A: It is given that,