If a particle moves in the xy-plane so that at time t > 0 its position vector is (In (t2 + 2t) , 2t2), then find its velocity vec- tor at time t = 2. | (3 1. 4 4 4. (5+) 5. 4 16 2. 3.

Q: (b) Amovingparticle starts at an initial positionr(0) = 1li + 2j +1k withinitial velocity v(0) = li…

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Q: A bee with velocity vector r' (t) starts out at (4, –4, –5) at t = 0 and flies around for 7 seconds.…

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Q: a. Find a parametrization of the curve x = (y* – 3)e2y.

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Find the tangential and normal components of acceleration at the given time t for the space curve…

A: Given curve is Now,

Q: At time t, a particle moving in the xy-plane is at position (x(t), y(t)), where x(t) and y(t) are…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: 4. For any time t 2 0, if the position of a particle in the xy-plane is given by x = r² +1 and y=…

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Q: 6. A particle moves in the xy-plane in such a way that its velocity vector is (1+1, 1). If the…

A: Find the position vector

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A: I am going to solve the given problem by using some simple calculus to get the required result.

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A: SOLUTION-

Q: 1. Find a parametrization for the line segment from (2, 1, 3) to (4,3, 2). 2. Find the velocity and…

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Q: Express the following as a vector valued function 7 (t). 1. The line L defined by y+3=3x and z+1 =0…

A: We will express the line L defined by y+3=3x and z+1=0 hyperbola -x2-2x+2y2+4y=-2 as a vector valued…

Q: Suppose that a particle following the path c(t) = (t,t – 5t,0) flies off on a tangent at to = 3.…

A: Given:c(t) = (t2 , t3-5t , 0)

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

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Q: 30. (2x + y²) dx + (2xy + 3y) dy C C: Any simple closed curve in the plane for which Green's Theo-…

A: We know that Green's theorem

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Q: find a parametrization c(t) of the curve satisfying the given condition. y = 3x − 4, c(0) = (2, 2)

A: It is given that,

Q: Find the orthogonal trajectories of the families of r e, where a being a parameter. (0)

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Q: 2. Show that the given vector functions are linearly dependent on (-0,00). e' x(t) = x, (t) = 4e 2e2…

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Q: 10. Draw the graph of the vector-valued functions (a) for the plane curve, r(t) = 2cost³i + 3sint³j,…

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Q: 25. A particle is located at (1, 1,0) at time t = 0 and it follows a path whose velocity vector is…

A: Let's find.

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Q: find a parametrization c(t) of the curve satisfying the given condition.  y = 3x − 4, c(3) = (2, 2)

A: To find the parametrization

Q: 6. Given the space curve r(t) = (t, 2et, e2t), find the tangential and normal components of…

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Q: 1. The acceleration of an object is a=2i+4j+6k.  Compute the position vector r(t) if the object at…

A: a=double derivative of position vector

Q: Find the tangential and normal components of acceleration at the given time t for the space curve…

A: Brief explanation of the answer has been provided in the file attached below. If you have any doubts…

Q: 1. Consider f(x, y) = 2x² – y² +3x– y and U is any unit vector in R?. Find the maximum value of D7f…

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Q: dy Let dt Draw a direction field with 9 points to justify your answer. a 2t² + 3y + 1. Which of the…

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Q: 3. A particle moving along a curve in the xy-plane has position (x(t1),y(t)), with x(1)= 2t +3sin t…

A: Velocity is equal to the first derivative of position vector   Let x =f1t and y =f2t then velocity…

Q: If the position vector (with its tail at origin) of a moving particle be t2i -2t + (t² +2t)k. then…

A: Differentiating position vector with time we get velocity vector. And differentiation of a vector…

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Q: 8. Find the curvature of the vector-valued function r(t) = at the point t = -1.

A: given function is rt=3t2,-4t,1t find the curvature at t=-1 k=r→'t×r→''tr→'t3

Q: 4y The divergence of the vector G = i+ sin y j+ 3k is :- -8y + cosy x3 الخيار 2 O

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Q: 5) The position vector of a particle is given by s(t) = 3t2 – 4t + 5.Find the time at which the…

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Q: E. Find the orthogonal trajectories to the curve y = ax²- acx (s held fixed. %3D where a

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

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Q: A. Express the following as a vector valued function 7 (t). 1. The line L defined by y+3=3x and z+1…

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Q: 3. Find the length of the trajectory of the vector valued function f(t) = (7V2 t, e",e-) from 0 to…

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Q: Given the position vector 7 (t) = of a particle in space at time t. t

A: Given,           The position vector r→t = t+1, t, 1t of a particle in space at time t.

Q: The Normal component of the acceleration of a moving object in space at time t is given by aN + 1 If…

A: Explained below

Q: time ?

A: Uploaded question :   The rocket is launched at time t = 0 with r (0)=2i-6j+4k. If the initial…

Q: 9. Find the directional derivative of f(x , y , z) = 3x° +y° +z° - 9x + 9y – 9z + 4 at the point 9.…

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Q: 6. Suppose that the temperature T at point (x, y,z) is given by the function T = 2x2 – y? + 4z², and…

A: Given temperature function is: T=2x2-y2+4z2 The tiny bug is at point 1,-2,1 Now, to find in which…