What is the relationship between the tangent unit vector and the orientation of a curve? Explain.

Q: How is the binormal vector related to the curve’s torsion? Give an example?

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Q: An object moves along a curve in the plane. What information do you gain about the motion of the…

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Q: Use the model for projectile motion, assuming there is no air resistance and  g = 32 feet per second…

A: Given Data: The gravitational acceleration is: g = 32 ft/s2 The initial height is: hi = 6 ft The…

Q: Give a vector valued function (see image 1) that traces out the line by using arclength as a…

A: Given: We have to write the  vector valued function that traces out the given line.

Q: Classify the stationary points of

A: For part (3) We have to classify the stationary points of the given function. For part (a) The given…

Q: Determine the point on the curve where the tangent is horizontal.

A:

Q: What is meant by a tangent vector?

A: To Explain:  a tangent vector

Q: find the equation of the tangent plane of this surface

A: In this question, we check the surface is simple and then we find the equation of tangent plane at…

Q: name another different type of 3-D curve from vector valued functions

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Q: Find an equation of the plane tangent to the surface

A: Given that : The equation is x2 + y 2 z 2 = 8 and the point P = ( 2, 2, 1).

Q: What is the derivative of a function ƒ(x, y) at a point P0 in the direction of a unit vector u? What…

A: For a function z=f(x,y): the partial derivative with respect to x gives the rate of change of f in…

Q: Determine whether the statement is true or false "If a particle moves along a sphere centered at the…

A: The given statements is “If a particle moves along a sphere centered at the origin, then its…

Q: (a) How do you find the slope of a tangent to a parametric curve?

A: (a) Assume a general parametric curve. Differentiate and find the derivatives.

Q: Represent the plane curve by a vector-valued function. y = (x − 2)2

A: y=x-22 Now let xt=t Now put xt=t in y=x-22, we get y=t-22

Q: sketch the curve ƒ(x, y) = c, together with ∇ƒand the tangent line at the given point. Then write an…

A: sketch the graph of x2-xy+y2=7

Q: Interpret the magnitude of the gradient vector at a point.

A:

Q: How do you find the tangent vector to a smooth curve at a point? How do you find the tangent line?…

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Q: Q5] What is a parametric representation of a curve? What is its advantage?

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

Q: What is a di¡erentiable curve’s unit tangent vector? Give an example.

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Q: Sketch the curve represented by the vector-valued function                               r(t) = ⟨…

A: Given  r(t) = ⟨ cos t, sin t ⟩

Q: What is a differentiable curve’s unit tangent vector? Give an example.

A:

Q: What are tangential components?

A: Consider the provided information, What are tangential components.

Q: (A) Find A vector tangent and normal for the curve: x3 y = + 5 2 at the point (1, 5.5)

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: Represent the plane curve by a vector-valued function y=1-x^2

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Q: a)What is the slope of the tangent line to the curve y=2sin4x  at x=⊼(pie)/4? b) Find a unit vector…

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Q: Explain Tangent Planes and Normal Lines?

A: According to the question, we have to define the term tangent plane and normal lines. The tangent…

Q: Explain in words the meaning of the curvature of a curve. Is it ascalar function or a vector…

A: According to the question, we have to explain the meaning of curvature of a curve. It is defined as…

Q: What formulas are available for writing a moving object’s acceleration as a sum of its tangential…

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Q: Explain Curvature of a Plane Curve?

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Q: Represent the plane curve by a vector-valued function y = 9 − x2

A: Given:y=9-x2The vector valued function for  a plane curve:rt=xti+ytj

Q: Explain unit tangent vector.

A: The Unit Tangent Vector The derivative of a vector valued function gives a new vector valued…

Q: Sketch a closed curve on a sheet of paper and draw a unit tangent vector T on the curve pointing in…

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Q: give two example of tangent vector on manifold

A: Manifold is a topological space that which is almost similar to a euclidean space near to each of…

Q: Write the application of Deravative" tangent and normal to a curve" also explain and with example.…

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Q: Compute for the tangential velocity of a wheel rotating at a speed of 2000 rpm such that the radius…

A: Formula for tangential velocity Vt is: Vt=2πrt  here r is the radius of the wheel and t is the time…

Q: How do i find the vertical/horizontal shift as well as the stretch

A: Let's understand the concept before getting into the solution. A function of the form: A.f(x)+b has…

Q: normal to the plane.

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Q: find the directional derivative of the function in the direction of the vector v

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Q: How do you find the Unit Tangent Vector to a curve C when you are given x(t) and y(t)? Where you are…

A: Suppose we are given a smooth curve C:r(t)→=<x(t),y(t)>on an openinterval I. Then a unit…

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

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Q: What is the curvature of a straight line?

A: Consider an equation of straight line, f(x)=mx+b Hence, f'(x)=m   and    f''(x)=0 Therefore,…

Q: Give a vector valued function (see image 1) that traces out the line but does not use arclength as a…

A: A vector valued function or a vector function for a 2-D plane is given by,…

Q: A plane flying at an altitude of 35,000 feet at a speed of 690 miles per hour releases a bomb. Find…

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Q: Explain the hyperbolic tangent function ?

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Q: Determine the moment of inertia about y-axis

A: This is a problem related moment of inertia of composite sections. Based on general formula and…

Q: Let L be the line with parametric equations

A:

Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.