The binormal vector to r(t) = (3sin t, 3 cos t, 4t) at t at t = is

Q: Given the vector function - r(t) = (t²- 4t)i + sin(2t − 4)3 + ( + ) Find the derivative of r(t). a)…

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Q: 3. Sketch the vector-valued function r(t) = (sin(2πt), t, 3 cos(2πt)), indicating direction.

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Q: Find the positive t when the vector r r(t) = (3t, 4t², 10t² - 4) is perpendicular to r'(t). t =

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Q: Define two vector functions 7(t) = 2 sin(t)i + 8 cos(t)j + t°k ü(t) = 8 sin(t)? + 2 cos(t)j + (t? –…

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Q: Determine the direction at t= pie/2 where R is 2sin t i + 2 cos t j + 2t k

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Q: Find the velocity and acceleration vectors in terms of u, and ug. de r= a sin 30 and =7t, where a is…

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Q: Ans. (5) Given position vector r(t) = (t₁ t - sint, 1- cast) ⇒ r (t) = ti + (t-sint) 3 + (1 - cost)…

A: Ans. (5) Given position vector

Q: If r(t) is the position vector of a particle in the plane at time t, find the indicated vector. Find…

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Q: Prove that the tangent vector is always orthogonal tothe position vector for the vector-valued…

A: Given r(t) =⟨sin t, sint cos t, cos2 t⟩.  we need to prove that the tangent vector is always…

Q: Sketch the curve which has the vector equation r(t) = cos ti + tj.

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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: Let the velocity vector be v(t) = (6 cos(3t), 8 exp(2t), 3t2). Compute the acceleration vector a(t).

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Q: Find the domain of the vector-valued function t R(t) = tan-¹t² + —_— 3 + sin t² k. 1-1²

A: Given the vector valued function R(t)=tan-1t i^+t1-t2j^+sin t2k^. We have to find the domain of…

Q: Let 7 (t) = (4t³ – 4, – 3e", – 3 sin( – 4t)) - Find the unit tangent vector T(t) at the point t = 0…

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Q: Find the directional derivative at (1, 1) if Vƒ(1, 1) = (3,−1) in the direction of the unit vector u…

A: Use the formula of directional derivative.

Q: Let 7(t) (-t + 5, 3e , - 5 sin( – 3t)) Find the unit tangent vector T(t) at the point t =0 T(0) --…

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