 11.R.1E: When do directed line segments in the plane represent the same vector?
 11.R.2E: How are vectors added and subtracted geometrically? Algebraically?
 11.R.3E: How do you find a vector’s magnitude and direction?
 11.R.4E: If a vector is multiplied by a positive scalar, how is the result r...
 11.R.5E: Define the dot product (scalar product) of two vectors. Which algeb...
 11.R.6E: What geometric interpretation does the dot product have? Give examp...
 11.R.7E: What is the vector projection of a vector u onto a vector v? Give a...
 11.R.8E: Define the cross product (vector product) of two vectors. Which alg...
 11.R.9E: What geometric or physical interpretations do cross products have? ...
 11.R.10E: What is the determinant formula for calculating the cross product o...
 11.R.11E: How do you find equations for lines, line segments, and planes in s...
 11.R.12E: How do you find the distance from a point to a line in space? From ...
 11.R.13E: What are box products? What significance do they have? How are they...
 11.R.14E: How do you find equations for spheres in space? Give examples.
 11.R.15E: How do you find the intersection of two lines in space? A line and ...
 11.R.16E: What is a cylinder? Give examples of equations that define cylinder...
 11.R.17E: What are quadric surfaces? Give examples of different kinds of elli...
Solutions for Chapter 11.R: University Calculus: Early Transcendentals 2nd Edition
Full solutions for University Calculus: Early Transcendentals  2nd Edition
ISBN: 9780321717399
Solutions for Chapter 11.R
Get Full SolutionsUniversity Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321717399. This textbook survival guide was created for the textbook: University Calculus: Early Transcendentals , edition: 2. Since 17 problems in chapter 11.R have been answered, more than 62297 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 11.R includes 17 full stepbystep solutions.

Angle of elevation
The acute angle formed by the line of sight (upward) and the horizontal

Complex conjugates
Complex numbers a + bi and a  bi

Components of a vector
See Component form of a vector.

Ellipse
The set of all points in the plane such that the sum of the distances from a pair of fixed points (the foci) is a constant

Gaussian curve
See Normal curve.

Identity function
The function ƒ(x) = x.

Inverse function
The inverse relation of a onetoone function.

Multiplicity
The multiplicity of a zero c of a polynomial ƒ(x) of degree n > 0 is the number of times the factor (x  c) (x  z 2) Á (x  z n)

Parameter interval
See Parametric equations.

Polynomial function
A function in which ƒ(x)is a polynomial in x, p. 158.

Product of matrices A and B
The matrix in which each entry is obtained by multiplying the entries of a row of A by the corresponding entries of a column of B and then adding

Quadrant
Any one of the four parts into which a plane is divided by the perpendicular coordinate axes.

Standard form of a polynomial function
ƒ(x) = an x n + an1x n1 + Á + a1x + a0

Sum of an infinite geometric series
Sn = a 1  r , r 6 1

Supply curve
p = ƒ(x), where x represents production and p represents price

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.

Unit ratio
See Conversion factor.

Unit vector
Vector of length 1.

Whole numbers
The numbers 0, 1, 2, 3, ... .