Let r(t) = (sin(2t), 3t, cos(2t)), t E [-T, "] be the position vector of a particle at time t. (a) Show that the velocity and acceleration vectors are always perpendicular. (b) Is there any time t for which r(t) and the velocity vector are perpendicular? Is so, find all such values of t.

Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of the…

A: Given function is, f(x,y)=sin(2x+y) and u=cos(-5π6)i+sin(-5π6)j⇒u=cos(5π6)i-sin(5π6)j=-32i-12j Now,…

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A: According to Bartleby q&a guidelines I will attempt only one question

Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of the…

A: Find your answer below

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A: Two vectors is perpendicular if their dot product is zero.

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Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of the…

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Q: 2. Let T(x; y) = sin(2x – y) , P (-; ) and Q(0;0) (a) Determine the directional derivative of T at P…

A: Tx,y=sin2x-y, P=-π3,π6,?=0,0                                      P1  P2                ?1,…

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Q: 3. A unit vector tangent to the curve y x2 at the point (2, 4).

A: We are entitled to solve only one question at a time so we will answer only the first question.…

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A: There is no such introduction for the solution.I have explained it within the solution.Please go…

Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of the…

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Q: Compute the principal unit tangent vector at t = T/2. F(t) = sin(2t) î + 2 cos(t) ĵ + tk COS 2 2 - -…

A: unit tangent vector

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Q: sin(t) et, X2 sin(t)- cos (t) and X3 D sin(t) + cos (t)] 0. Given that X, cos(t) sin(t) + cos (t)|…

A: The problem is wrong, three vectors are not linearly independent.

Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of the…

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Q: 10. A particle moves in the xy-plane so that the position of the particle is given by x(1) =1+cos t…

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Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of the…

A: Answer is given below

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Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of the…

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A: position vector of a particle in the xy-plane is given by < t^2+1, ln(2t+3) > for all t>=0

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Q: If g is the vector-valued function defined by g (t) = (sin(2t), cos(3t)), then g' (t) = %3D

A: Given : gt = sin2t, cos3t

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Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of the…

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Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of the…

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Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of the…

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Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of the…

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