Consider a particle moving with a trajectory given by r(t)=x(t)i +y(t)j+z(t)k Discuss all changes in position, velocity and acceleration of the particle is assumption is given by vector function r2(t)=r(2t).

Q: Find the directional derivative of the function f(x, y) = xy at the point (x, y) = (-4,-6) in the…

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Q: of f(x, y, tion of ve

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Q: QI-A) Fnd the position, vekocity and the speed of the vector function ( r(t) ) that given bekow at…

A: Given vector function is r(t)→=t2i-t3j To find the position, velocity and the speed of the vector…

Q: (a) F(t)=(2 sint)i + (2 cost)j from the point A(2, 0) to the point B(-2, 0)

A: To find the arc length of given function

Q: What is the graph of r(t)=2 costi + sintj?

A: Vector-valued function : It is a function of the form  r(t)=f(t)i⏜+g(t)j⏜ or…

Q: 8) Find a unit vector in the direction that f(x, y, z)=2x² +6xz²-yz³ increases most rapidly at the…

A: Given: A function fx , y , z=2x2+6xz2-yz3. To Find: Unit vector in the direction of the given…

Q: For each problem, calculate the directional derivative in the given direction and the gradient…

A: z=x2-6y2  To Find: Directional derivative and gradient vector at P(7,2) in the direction of  a)…

Q: 42. Two boats B, and B2 are moving with velocities (4i – 3j + 7k) ms' and (2i + 3j + 4k) ms…

A: Velocities (4i-3j+7k) and (2i+3j+4k)

Q: Consider the function f(x.y) = x(/y +x) and the point P (3,9). (a) Find the gradident vector of f at…

A: The function f(x,y)=xy+x and the point P=3,9. We have to answer the following...

Q: the position vector r describes the path of  an object moving in space. (a) Find the velocity…

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Q: Q4 (a) Given a cylinder x' +y² = 1 and a plane x +z = 1. (i) Find a vector-valued function r(t) that…

A: we have,  A cylinder x2+y2=1 and a plane x+z=1 i x2+y2=1x2+y2=cos2t+sin2tx2+y2=cost2+sint2⇒x=cost,…

Q: Let x' = [4, 2, 1] and y' = [-1, 3, 0]. (a) Find 2x+y. (b) Find x'y. (c) Find the length of x, Lx.…

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Q: The position vector r describes the path of an object moving in the xy-plane. Position Vector Point…

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Q: (3) This problem will walk you through the steps of finding a directional derivative through the…

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Q: The answer I provided for (x-5)^2 is said to be wrong. Please help me rectify the problem. Also…

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Q: \ Let v = (v, v2) be a direction vector on a line . The number 8 %3D defined to be the slope of the…

A: This is a problem of geometry and vector algebra.

Q: Suppose that the vector-valued function F(t) = < 3t, cos(5t), sin(5t) represents the position of an…

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Q: The directional derivative of f(x, y, z) = xyz at point (-1, 1, 3) in the direction of vector î - 2ĵ…

A: Remark: We know that the directional gives the rate of change of a function at a specific point in…

Q: Find the maximum rate of change of f(x, y, z) = x+y/z at the point (1, -3, 5) and the direction in…

A: We will find the maximum rate of change and the direction.