Find a vector normal to the plane with the given equation. 3(x – 5) – 5(y – 1) + 10z = 0 n =

Q: 1. r(t) = (1+ t)³/2i+ (1 – t)³/2j+ tk is the position of a particle in space at time t. Find the…

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Q: Q2. A particle is moving along the curve whose position vector is given as R(1) = (1) i + ( In…

A: Given

Q: The position of a particle moving in space at time t>=0 is r(t) = 2i + (4 sin t/ 2) j + (3 -…

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Q: If an object follows the path of the two-dimensional vector-valued function p(t)=(16−cos(t),…

A: Given p(t)=(16−cos(t), 0.6πt−0.15t2−3)

Q: 4. Let r(t) = (t)i + (t-16t²) ; be the position of a particle in a plane at time t. Find the angle…

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Q: (b) Suppose that the position vector of a particle moving in the plane is r-12vii+j, t>0. Find the…

A: This is application of derivative problem

Q: Q2) Find T N „B of the vectors the curve r(t) = at the point (1, ,1)

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Q: The paths r(t)=(12, t3)" (t) = (t", t") and r1(t)=(t4, t6)"1 (t) = (e", t") trace the same curve,…

A: Given : rt=t2,t3 r1t=t4,t6

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

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Q: Find the position function of a particle moving along a coordinate line that satisfies the given…

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Q: Q2) Find the vectors the curve r(t) = at the point (11) of

A: First of all find r'(t) and the length of r'(t). Here, r'(t)=<2t,2t2,1> |r'(t)|=4t2+4t4+1…

Q: 6. Compute the Divergence and Curl of the following vector F:F = yze#vi + xze#¥j+(e™y + 3 cos 32)k…

A: Use divergence and curl formula Compare hyperbola with standard equation of hyperbola

Q: 2t + 3 r(t) = -, In(t² + 2) t² +1' describes the position of a particle in the plane, for t> 0.…

A: We have to find the unitary tangent vector at t=2.

Q: 8. D is a curve that is represented by the vector function H(t) =< t² + 5,1 – 4t,; A. Determine an…

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Q: Suppose that a particle follows the path r(t) = 2 cos(3t)i+ jsin(3r) – ť² k. Determine the velocity…

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Q: Q2/ find the parametic equation for the line passi through the pont (o,1,2) that is parallel to the…

A: To find parametric equation

Q: Find a vector equation and parametric equations in t for the line through the point and…

A: Given that the point that posses through the line and the line perpendicular to the plane is, P 0 =…

Q: For time 1 > 0, the position of a particle moving in the xy-plane is given by the parametric…

A: Velocity==rate of change of distance per unit time=displacementtime=dsdt. Given that: x=4t+t2  and…

Q: 3. A particle moves in the xy-plane so that at any time t, its coordinates are given by x = t° -1…

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Q: d the normal vector to the surface y = 16x at (4,8). (a) 16(f-j) (b) (1 – f) (c) 6(1 – 1) (d) none…

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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: 3. (a) At any point of the curve z = t, y = t², z = 3³. Find the unit tangent vector and unit normal…

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Q: The curve of the vector function r(f) =/3 costi-2sintj, 0<t<2T is the ellipse 3 x² y? = 1 4 2y2 the…

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Q: For time t> 0, the position of a particle moving in the xy-plane is given by the vector (, e3t) .…

A: Option e is true.

Q: 3. Find the length of the trajectory of the vector valued function f(t) = (7V2.1,7",e-7) from 0 to…

A: The detailed solution of the problem is given in the next steps.

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: Find the position vector for a particle with acceleration, initial velocity, and initial position…

A: Given,

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: B) The vector v = (3cost)i + (3sint)j +t2k .gives the position of a moving body at time t. find the…

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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…

Q: find The unit Vectors tangent and normal toThe ellipse x+ 2y=6 6at The Point (2,1).

A: I am going to solve the give problem by using some simple geometry to get the reuired result.

Q: A bee with velocity vector r' (t) starts out at (2, 5, -2) at t = 0 and flies around for 1 seconds.…

A: We can answer first question as per the honor policy. Please resubmit other parts as well to know…

Q: O Solve the electric flux through a paraboloid z =x² + y² – 16 that lies below plane z = 0. It is…

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Q: Find rCt) amd the velocity a Ct). = s 5 et,16t, 22t +8>, the initial velocity v C0) = T 1,0, 1>, and…

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Q: If two objects travel through space along two different curves, it's often important to know whether…

A: If they collide on any point then at the point both the vectors must be equal.

Q: Find the binormal vector for 7(t) = (3t, sint, cos t) А. ВО cost, sint V10 10 1 B(e) = (- 3 В. ВО)…

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Q: 3x2 – 4y2 at which the vector 11. Find the points on the graph of z = (3, 2, 2) is normal to the…

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Q: 1. The position of a particle moving in the ry plane at time t units is given by the vector equation…

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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: Q1) Transform the vector to cylindrical coordinate system: - K= yx'+ xy + (x²/Vx²+y*)z°

A: Hello. Since your question has multiple parts, we will solve the first question for you. If you want…

Q: Q.1 Find the parametric equation of the line that 1) Let L1: x = 2t – 1, y = 3 +t,z = t – 1/2 Find…

A: Given parametric equation of line  x=2t-1 y= 3+t  z= t-1/2   As per our guidelines we are supposed…

Q: Consider the curve = (e', e*, 4t) . r = The component, in the direction of the vector (-1, 1, 2), of…

A: For a curve: r(t), the velocity vector v(t) is calculated using the formula: v(t)=ddtr. The…

Q: F(x, y) = (3x-4y2i+6yj by the force in moving a particle in the positive direction once around the…

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Q: For t > 0, a particle moves in the xy-plane with position vector (x (t), y (t)), where x (t) = te-t…

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Q: The position of a particle in the xy-plane at time t is r(t) = (t+ 1) i + (t +3) j. Find an equation…

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Q: 2.) a.) y=fcx), X=t y = f (t) the vector egn of the plane curve is ずul-t+fc+)+o.g は13

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Q: (iii) Find a vector equation for the tangent line to the curve of intersection of the cylinder a² +…

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Q: The path r(t) = (t) i + (2t +5) j describes motion on the parabola y = 2x + 5. Find the particle's…

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