10. Consider the vector-valued function given by r(t) = (√2t, et, e-t). Compute T, N, and the curvature K.

Q: 2. Given r(t) = (31²,1³,-1²) find the following using vector operations. a) the unit tangent vector…

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Q: r(t) = (3√2t, e³t, e-3t) (a) Find the unit tangent and unit normal vectors T(t) and N(t). 3√2e³x +…

A: Question (1) (a) We need to find the unit tangent and unit normal vector T(t) and N(t) of the vector…

Q: Consider the vector function r(t) that has unit tangent vector 1 T(t)= (1,1,2t), 0≤t≤ 2. √1+5t²…

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Q: 6. Find a vector which is normal to the currive: 3= 11 at (1,2). x³ + xy + y²

A: We have to find a vector which is normal to the curve: x³ + xy + y³ = 11 at (1,2).

Q: Let R be a vector-valued function such that R(0) = (0,2,1-2√2) and for every te R, R' (t) = (2√2…

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Q: 3. Determine the curvature of r(t) =(√2 t, e²,e-).

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Q: For the given vector-valued function below, find its (i) unit tangent vector, (iii) binormal vector,…

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer one question at a…

Q: 86. The unit nomal vecter to the curwe x?+y2 + Z² = 4 at (1,1,1) is %3D fa) li+aj+k)NI fb) lit2j+k)…

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Q: Find the unit tangent and unit normal vectors T(t) and Ñ(t) given 7(t) = (3/2t, e3t, e¬3t). Also,…

A: Given that r→t=32t,e3t,e-3t. Find the value of r→'t and r'→'t.…

Q: A smooth curve C' is defined by some vector function R(t) with R = (π, 0, -2) and R¹(t) = (2, √5 csc…

A: Disclaimer: Since, you have requested for the answer of part 3, only part 3 has been answered.…

Q: Let be a curve defined by the vector function (t)= 6ti + çin 2t -cos 2+ k 3- and Find the moving…

A: Let C1 be a curve defined by the vector function R→(t)=6ti→+sin2tj→-cos2tk→. Find the moving…

Q: A smooth curve C is defined by some vector function R(t) with R (-) = (7,0,−2) and R′(t) = (2, √5…

A: Introduction: The moving trihedral of a vector curve is its unit tangent vector, unit normal vector…

Q: 2. Consider the following vector function: r(t) = = a cos wti + a sin wtj + bwtk, where a, b and w…

A: We need to find radius of curvature.

Q: 5. Let 7(t) =. a. Find the domain of the vector function. b. Evaluate lim1 7(t).

A: (a). r→(t)=3et-1t, t3-t2t-2, sin(πt)ln t

Q: Next Consider the two vector-valued functions given by r(t) = (t+1, cos 1+t w(+) = (*, sin() *) . a.…

A: (a) The two vector valued functions intersect if r(a) = w(b) for some t = a and s = b.…

Q: B. Given that r (t) = (3t cos t) j - (3t sint) k , is the position vector of a moving particle, find…

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Q: Q3) For the vector function f(t) = [2e", te?, 3 te? 1, Determine the point of %3D tangency and the…

A: We have to find the point of tangency and unit tangent vector at t=2.

Q: Q2) Find the vectors „N of the curve r(1) = ) at the point (1.1)

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Q: 4. Given r(t) =ti+t²j. Find the unit tangent vector and principal unit normal vector when t=1.

A: Solution :-

Q: 3. Compute the tangent plane at u = 0 and v=0.

A: Introduction: The formula of the tangent plane of the function f(x,y) at the point a,b is given by,…