1 and 2 please 1. Give an example of a vector field F(x, y) in 2-space such that F has constantdirection but || F is not constant.2. Give an example of a vector field F(x, y) in 2-space such that ||F|| is constant butF is not constant.3. Write a formula for a vector field in which all vectors are parallel to the x-axis andall vectors on a vertical line have the same magnitude.4. Write a formula for a vector field in which all vectors point toward the origin andhave constant length.5. Write a formula for a vector field in which all vectors are of unit length andperpendicular to the position vector at that point.6. Show that the acceleration a of an object flowing in a velocity field F(x, y)u(x, y) 7+ v(x, y) 3 is given by a = (Uzu+ uyv)i+ (vzU + vyv) j.%3D7. Show that every flow line of the vector field = xi-yj lies on a level curve forthe function f(T,y) = ry.8. Show that every flow line of the vector field = yi+xj lies on a level curve forthe function f (x, y) = x2 -y².

1. Give an example of a vector field F(x, y) in 2-space such that F has constant direction but || F is not constant. 2. Give an example of a vector field F(x, y) in 2-space such that ||F|| is constant but F is not constant.

1. Give an example of a vector field F(x, y) in 2-space such that F has constant direction but || F is not constant. 2. Give an example of a vector field F(x, y) in 2-space such that ||F|| is constant but F is not constant.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter8: Applications Of Trigonometry

Section8.4: The Dot Product

Problem 48E

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Question

1 and 2 please

1. Give an example of a vector field F(x, y) in 2-space such that F has constant
direction but || F is not constant.
2. Give an example of a vector field F(x, y) in 2-space such that ||F|| is constant but
F is not constant.
3. Write a formula for a vector field in which all vectors are parallel to the x-axis and
all vectors on a vertical line have the same magnitude.
4. Write a formula for a vector field in which all vectors point toward the origin and
have constant length.
5. Write a formula for a vector field in which all vectors are of unit length and
perpendicular to the position vector at that point.
6. Show that the acceleration a of an object flowing in a velocity field F(x, y)
u(x, y) 7+ v(x, y) 3 is given by a = (Uzu+ uyv)i+ (vzU + vyv) j.
%3D
7. Show that every flow line of the vector field = xi-yj lies on a level curve for
the function f(T,y) = ry.
8. Show that every flow line of the vector field = yi+xj lies on a level curve for
the function f (x, y) = x2 -y².

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