Prove that the vector T'(t) = 0 for moving in a straight line

Q: Evaluate along the curve y=x2 from (-1,1) to (2,4). First find the vector valued function r(t)…

A: Curve length problem..

Q: 4. Find the directional derivative of f in the direction of vector v at point (1,3) such that v =…

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Q: Find the point on the graph of z = 3x2 + 2y at which vector (24, 8, 2) is normal to the tangent…

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Q: Find the parametric equations of the tangent line to the curve represented by the vector function…

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Q: find the velocity and acceleration vectors in terms ofur and uθ .1. r =θ and dθ/dt = 2

A: Given, r=θ and dθdt=2   Find Velocity and acceleration vectors in terms of ur and uθ:

Q: Find the direction in which the maximum rate of change occurs for the function f(x, y) = 3x sin(xy)…

A: NOTE: Refresh your page if you can't see any equations. . take the partial derivative with respect…

Q: find a vector parametrization for the line with thegiven description. Passes through (1, 1, 1) and…

A: The vector parametrization is:                                       r(t) = r0 + tv = x0,y0,z0 +…

Q: What is special about the derivatives of vector functions of con-stant length? Give an example.

A: What is special about the derivatives of vector functions of constant length

Q: 2. Suppose that f (1,2) = 3 and that the directional derivative of ƒat point (1,2) in the direction…

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Q: 3. Show that if a particle moves with constant speed, then the velocity and acceleration vectors are…

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Q: Find a unit vector in the xy-plane that is orthogonal to

A: Here given vector as a=123 Consider a vector as b=25-150 Now find the dot product of vector b to…

Q: Suppose that f (1,2) = 3 and that the directional derivative of f at point (1,2) in the direction of…

A: Given : f1,2=3 and the directional derivative of f at 1,2 in the direction of the vector i+j is…

Q: find a vector parametrization for the line with thegiven description. Passes through O and (4, 1, 1)

A: To findvector parametrization passes through O and (4,1,1)

Q: Sketch a few representative vectors of vector field F = ⟨0, 1⟩along the line y = 2.

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Q: Let F(x, y, z) =2x2+3y2+4z2. For which unit vector 0 will the directional derivative DoF at…

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Q: Find the directional derivative of f(x, y, z) (2,1,3) in the direction of a vector making an angle…

A: Given the function f(x,y,z)=zx+y4

Q: Prove that the vector given by (sin ysinh x + cos ycosh x) i + (cos y cosh x- sin ysinh x) j is a…

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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.…

Q: Suppose ƒ is differentiable at (9, 9), ∇ƒ(9, 9) = ⟨3, 1⟩, and w = (1, -1). Compute the directional…

A: Given that ∇ƒ(9, 9) = ⟨3, 1⟩. Note that w = (1, -1) is not a unit vector. Its unit vector along same…

Q: Show that if a particle moves with constant speed, then the velocity and acceleration vectors are…

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Q: Find the work done by the force F- Tyi + (y - ±)j over the straight line from (0,0) to (3,6).

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Q: It is known that the acceleration vector for a particle is given by A(t) = 4j + 2tk. Determine the…

A: We need to determine vector equation of curve traced.

Q: Represent the plane curve by a vector-valued function. 2x − 3y + 5 = 0

A: Given: 2x-3y+5=0 for finding given equation in vector form, we assume x=t and find value of y in…

Q: Find a vector in the plane parallel to the line ax + by = c.

A: We know that, Slope of parallel lines are equal Given equation of line is ax + by = c Slope of this…

Q: Which of the following vector functions represents the curve of intersection of the cylinder x2 +y =…

A: Given Data: The equation of the curve is: x2+y2=4 ......1 The equation of the plane is: x+z=3…

Q: Express the unit vector directed toward the origin from an arbitrary point on the line described by…

A: solution : Given the point x=0, y=3 and z1.22unit vector is defined…

Q: Find the directional derivative of in the direction of the vector (1,3) at the point (-1,2)

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Q: Find First and second derivatives of Funchion . tm - (e-a -a)(e-a+a) Where a is parameber

A: To find a first and second derivative by first simplify the equation and finding it's value at x=0

Q: Suppose that the directional derivative of a function f at a point P in the direction of the vector…

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Q: Find the two-unit vectors that are parallel to the tangent line to the curve y =x2sin(x) at the…

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Q: 2. If a particle moves in the xy-plane so that at any time t > 0, its position vector is (In(r² +…

A: Solution-

Q: Find the Directional Derivabive of Pary,2)= x-yz'+ at the point CI, -2, 0) in the direcbion of…

A: A scalar function is a rule to associate a number to a particular point in space. The directional…

Q: Show that whether the functions sint and cost in the vector space C[-n, 1]of continuous functions on…

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Q: Find a vector equation for the tangent line to the curve of intersection of the cylinders x2+y2=25…

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Q: find the velocity and acceleration vectors in terms ofur and uθ . r = a(1 - cos θ) and dθ/dt = 3

A: Velocity is defined as the rate of displacement. Acceleration is known as the rate of change in…

Q: The position vector of a particle in the xy-plane is given by for all t > 0. The acceleration…

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

Q: (#2) Evaluate the directional derivative Duf (3, 4) if f (x,y) = Vx² + y² and u is the unit vector…

A: The expression for the directional derivative of the function f in the direction of u at a point…

Q: The largest value of the constant b such that the vector-valued function F(t) =< cos 21It, sin (t-…

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Q: Let f (x,y,z) = xye² + yze*. From point (1,0,1), which unit vector points in the direction in which…

A: Consider the given information. fx,y,z=xyez+yzex The point is 1,0,1. The direction in which f…

Q: Is it always true that T(0) = 0 where the zero vectors live in the appropriate spaces? Justify

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Q: Find the directional derivative Duf(1, 1), where f(x, y) = x2 + y2 and u is the unit vector at an…

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Q: Q1. Find the directional derivative of = x²z + 2xy² + yz2 at (1, 2,-1) in the direction of vector…

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Q: When is a vector incomprehensible and when is a vector irrational?

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Q: Find the linear equation of the plane through the point (2, −2, 6) and with normal vector j+2k.

A: Explanation of the solution is given below...

Q: Find the a unit vector in the direction of which f(x, y) = In (1 + xy) increases the most rapidly at…

A: Consider the given function as fx,y=ln1+xy

Q: Let f(x, y) = 5y² ln(4x). Then Duf(1,4) in the direction of the vector (-2, –2) is

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Q: Suppose a vector function F(x, y) = 3xi + 2xyj + y ln zk moves along a path C where x = t2, y = t +…

A: The formula to find the work done by the vector function helps to find the required work done. The…

Q: Prove that the directional derivative of flay.2) = aysinz. direction v=i +2j+2k 1Is Sin Z at…

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Q: Find the divergence and curl of the vector A = rz sin ø ↑ + 3rz² cos o and evaluate both answers at…

A: Consider the given vector. A=rzsinϕr^+3rz2cosϕϕ^ The divergence formula is defined as. divF=Px+Qy…

Q: The gradient vector of g(x, y) = at (√√2,-1) is Vg(√2, -1) is equal to Select one: O True O False -

A: Given: The gradient vector of g(x,y)=x22-y22 at (2,1) is ∇g(2,1) is equal to &lt;2,1&gt;

Magnitude

A vector is an element with both direction and magnitude. A vector is represented using an arrow, where the arrow represents the direction of the vector and its length is represented using the magnitude. The set of vectors in space is known as vector space. The vectors can be added, subtracted, multiplied, and divided in a vector space. The image below shows a vector AB.