Calculo 2 De dos variables_9na Edición - Ron Larson

11 En
This
este
chapter
capítulo
introduces
se introducen
vectors
los
and
vectores
the
three-dimensional
y el sistema de
coordinate
coordenadas
system.
tridimensional.
This Vectors chapter are
Los
used introduces vectores
to represent vectors se usan
lines and para
and the
three-dimensional representar
planes, and are
rectas
also coordinate y
used
planos,
to represent
y system. también
Vectors para
quantities
representar are such used as to cantidades
force represent and velocity.
como lines and fuerza
The
planes, y
three-dimensional
velocidad. and are El also sistema
coordinate used de to coordenadas represent system is used
quantities tridimensional
to represent such surfaces as se force utiliza
such and para
as velocity. ellipsoids
representar The and
three-dimensional superficies
elliptical cones.
como
Much
elipsoides coordinate of the
y
material system conos is elípticos.
used
to in represent the
Gran
remaining
parte surfaces chapters
del such material as relies ellipsoids en
on
los
an
capítulos
and
elliptical understanding
restantes cones. of
se Much this
fundamenta
system. of the material en el
in entendimiento the remaining de chapters este sistema. relies on an
understanding En
In this
este
chapter,
capítulo, of you this se aprenderá:
should system. learn the
following.
In ■ this Cómo chapter, escribir you vectores, should learn realizar the operaciones
■
following. How to write
vectoriales
vectors,
básicas
perform
y representar
basic
vector operations,
vectores de
and
manera
represent ■
gráfica.
■ How vectors write
(11.1)
graphically. vectors, (11.1) perform basic
vector operations, and represent ■
■ How to plot points in a three-dimensional
■ vectors Cómo determinar graphically. puntos (11.1)
coordinate system and analyze
en un
vectors
sistema
■ How in space.
de to coordenadas plot (11.2) points in tridimensional a three-dimensional y
coordinate analizar vectores system en and el analyze espacio. vectors (11.2)
■ How to find the dot product of two
■ in
vectors
Cómo space. encontrar (11.2)
(in the plane
el producto
or in space).
escalar
(11.3)
■ How de dos to vectores find the dot (en product el plano of y two en el
■ How
espacio).
to find
(11.3)
the cross product of two
vectors (in the plane or in space). (11.3)
vectors (in space). (11.4)
■ How Cómo to encontrar find the cross el producto vectorial of twode
■ How
dos vectores
to find equations
(en el espacio).
of lines
(11.4)
and planes
vectors (in space). (11.4)
in space, and how to sketch their graphs.
■ How (11.5)
Cómo to encontrar find equations las ecuaciones of lines and deplanes
in rectas space, y planos and how en to el sketch espacio, their y cómo graphs.
■ How
dibujar
to recognize
sus gráficas.
and
(11.5)
write equations
(11.5)
of cylindrical and quadric surfaces and
■ How of
Cómo
surfaces to reconocer recognize of revolution. and y escribir write (11.6) equations ecuaciones
of de cylindrical superficies and cilíndricas quadric surfaces y cuadráticas and
■ How
y las
to
superficies
use cylindrical
de revolución.
and spherical
of surfaces of revolution. (11.6) (11.6)
coordinates to represent surfaces in
■ How space.
Cómo to (11.7)
utilizar use cylindrical coordenadas and spherical cilíndricas
coordinates y esféricas to para representar surfaces superficies in
space. en el espacio. (11.7) (11.7)
Vectors Vectores and y la the geometría
Vectors and the
Geometry del espaciof Space
Geometry of Space
Mark Hunt/Hunt Stock
Two Dos remolcadores tugboats are pushing están empujando ocean liner, un barco as shown trasatlántico, above. Each como boat se muestra is exerting en la
Mark Hunt/Hunt Stock
■ a foto. force Cada of 400 barco pounds. ejerce What una fuerza is the resultant de 400 libras. force on ¿Cuál the es ocean la fuerza liner? resultante (See en el
Two Section barco tugboats trasatlántico? 11.1, are Example pushing (Ver 7.) la an sección ocean liner, 11.1, as ejemplo shown above. 7.) Each boat is exerting
■ a force of 400 pounds. What is the resultant force on the ocean liner? (See
Section 11.1, Example 7.)
v
v
u
u
v
u
u
v
u
u
u + v
u + v
v
v
Vectors indicate quantities that involve both magnitude and direction. In Chapter 11, you will study operations of vectors
in the plane and in space. You will also learn how to represent vector operations geometrically. For example, the graphs
Los shown Vectors vectores above indicate indican represent quantities cantidades vector that addition involve que implican in both the magnitude plane. tanto magnitud and direction. como dirección. In Chapter En 11, el you capítulo will study 11 se operations estudiarán of vectors operaciones
in the plane de vectores and in en space. el plano You will y en also el espacio. learn how También to represent aprenderá vector operations cómo representar geometrically. operaciones For example, de vectores the graphs de
manera shown above geométrica. represent Por vector ejemplo, addition las gráficas in the plane. que se muestran arriba representan adición de vectores en el plano.
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