 12.1: What is the difference between a vector and a scalar?
 12.2: How do you add two vectors geometrically? How do you add them algeb...
 12.3: If a is a vector and c is a scalar, how is ca related to a geo metr...
 12.4: How do you find the vector from one point to another?
 12.5: How do you find the dot product of two vectors if you know their le...
 12.6: How are dot products useful?
 12.7: Write expressions for the scalar and vector projections of b onto a...
 12.8: How do you find the cross product a _ b of two vectors if you know ...
 12.9: How are cross products useful?
 12.10: (a) How do you find the area of the parallelogram deter mined by a ...
 12.11: How do you find a vector perpendicular to a plane?
 12.12: How do you find the angle between two intersecting planes?
 12.13: Write a vector equation, parametric equations, and sym metric equat...
 12.14: Write a vector equation and a scalar equation for a plane.
 12.15: (a) How do you tell if two vectors are parallel? (b) How do you tel...
 12.16: (a) Describe a method for determining whether three points , , and ...
 12.17: (a) How do you find the distance from a point to a line? (b) How do...
 12.18: What are the traces of a surface? How do you find them?
 12.19: Write equations in standard form of the six types of quadric surfaces.
 12.20: Determine whether the statement is true or false. If it is true, ex...
 12.21: Determine whether the statement is true or false. If it is true, ex...
 12.22: Determine whether the statement is true or false. If it is true, ex...
 12.23: Determine whether the lines given by the symmetric equations and ar...
 12.24: (a) Show that the planes and are neither parallel nor perpendicular...
 12.25: Find an equation of the plane through the line of intersection of t...
 12.26: (a) Find an equation of the plane that passes through the points , ...
 12.27: Find the distance between the planes and .
 12.28: Identify and sketch the graph of each surface.
 12.29: Identify and sketch the graph of each surface.
 12.30: Identify and sketch the graph of each surface.
 12.31: Identify and sketch the graph of each surface.
 12.32: Identify and sketch the graph of each surface.
 12.33: Identify and sketch the graph of each surface.
 12.34: Identify and sketch the graph of each surface.
 12.35: Identify and sketch the graph of each surface.
 12.36: Identify and sketch the graph of each surface.
 12.37: An ellipsoid is created by rotating the ellipse about the axis. Fi...
Solutions for Chapter 12: VECTORS AND THE GEOMETRY OF SPACE
Full solutions for Multivariable Calculus,  7th Edition
ISBN: 9780538497879
Solutions for Chapter 12: VECTORS AND THE GEOMETRY OF SPACE
Get Full SolutionsThis textbook survival guide was created for the textbook: Multivariable Calculus,, edition: 7. Chapter 12: VECTORS AND THE GEOMETRY OF SPACE includes 37 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. Since 37 problems in chapter 12: VECTORS AND THE GEOMETRY OF SPACE have been answered, more than 22587 students have viewed full stepbystep solutions from this chapter. Multivariable Calculus, was written by and is associated to the ISBN: 9780538497879.

Algebraic model
An equation that relates variable quantities associated with phenomena being studied

Blind experiment
An experiment in which subjects do not know if they have been given an active treatment or a placebo

Categorical variable
In statistics, a nonnumerical variable such as gender or hair color. Numerical variables like zip codes, in which the numbers have no quantitative significance, are also considered to be categorical.

Causation
A relationship between two variables in which the values of the response variable are directly affected by the values of the explanatory variable

Demand curve
p = g(x), where x represents demand and p represents price

Dihedral angle
An angle formed by two intersecting planes,

Domain of a function
The set of all input values for a function

Doubleangle identity
An identity involving a trigonometric function of 2u

Elements of a matrix
See Matrix element.

Graph of a relation
The set of all points in the coordinate plane corresponding to the ordered pairs of the relation.

Hyperboloid of revolution
A surface generated by rotating a hyperbola about its transverse axis, p. 607.

Midpoint (in a coordinate plane)
For the line segment with endpoints (a,b) and (c,d), (aa + c2 ,b + d2)

Quotient identities
tan ?= sin ?cos ?and cot ?= cos ? sin ?

Range screen
See Viewing window.

Scientific notation
A positive number written as c x 10m, where 1 ? c < 10 and m is an integer.

Sinusoid
A function that can be written in the form f(x) = a sin (b (x  h)) + k or f(x) = a cos (b(x  h)) + k. The number a is the amplitude, and the number h is the phase shift.

Solution of an equation or inequality
A value of the variable (or values of the variables) for which the equation or inequality is true

symmetric about the xaxis
A graph in which (x, y) is on the graph whenever (x, y) is; or a graph in which (r, ?) or (r, ?, ?) is on the graph whenever (r, ?) is

Terminal side of an angle
See Angle.

Xmax
The xvalue of the right side of the viewing window,.