Vector calculus Please solve part (d) and (e) A parametric curve C is given by the position vectorr(t)sin (2t), sin (t),e'Osis".2a) Find the tangent vector at the point P given byt =4b) Determine the tangent component of the accelerationvector and the normal component in P.c) c) A thread has the shape given by the curve C, andmass per. length given by the function2z?8(z) =-(1+z*)* *Calculate the mass of the thread.d) A vector field is given byF(x,y,z) = 2xj+2(1-eri (** -y(1-y)Ā.Find the work that the vector field performs by movingfrom start to finish point alongcurve C.e) Calculate the total work that the vector field does bywalking along C from start to end pointthen move along a straight line back to the startingpoint.Can you determine if the vector field is conservativejust by calculating this working integral? Justify theanswer.

To solve d and e: A vector field is given by, The parameterized curve C is given by, The interval…

d) A vector field is given by F(x,y,2) = 2xj+ (x² - y(1-y))k . 2(1-e"?) Find the work that the vector field performs by moving from start to finish point along curve C. e) Calculate the total work that the vector field does by walking along C from start to end point then move along a straight line back to the starting point. Can you determine if the vector field is conservative just by calculating this working integral? Justify the answer.

d) A vector field is given by F(x,y,2) = 2xj+ (x² - y(1-y))k . 2(1-e"?) Find the work that the vector field performs by moving from start to finish point along curve C. e) Calculate the total work that the vector field does by walking along C from start to end point then move along a straight line back to the starting point. Can you determine if the vector field is conservative just by calculating this working integral? Justify the answer.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section11.5: Polar Coordinates

Problem 98E

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Concept explainers

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.

Question

Vector calculus

Please solve part (d) and (e)

A parametric curve C is given by the position vector
r(t)
sin (2t), sin (t),e'
Osis".
2
a) Find the tangent vector at the point P given by
t =
4
b) Determine the tangent component of the acceleration
vector and the normal component in P.
c) c) A thread has the shape given by the curve C, and
mass per. length given by the function
2z?
8(z) =-
(1+z*)* *
Calculate the mass of the thread.
d) A vector field is given by
F(x,y,z) = 2xj+
2(1-eri (** -y(1-y)Ā.
Find the work that the vector field performs by moving
from start to finish point along
curve C.
e) Calculate the total work that the vector field does by
walking along C from start to end point
then move along a straight line back to the starting
point.
Can you determine if the vector field is conservative
just by calculating this working integral? Justify the
answer.

Calculus that deals with differentiation and integration of the vector field in three-dimensional Euclidean space. It deals with quantities that have both magnitude and direction.

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