- 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
Angle of elevation
The acute angle formed by the line of sight (upward) and the horizontal
Complex numbers a + bi and a - bi
Components of a vector
See Component form of a vector.
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
See Normal curve.
The function ƒ(x) = x.
The inverse relation of a one-to-one function.
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)
See Parametric equations.
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
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 + an-1x n-1 + Á + a1x + a0
Sum of an infinite geometric series
Sn = a 1 - r , |r| 6 1
p = ƒ(x), where x represents production and p represents price
symmetric about the x-axis
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 Conversion factor.
Vector of length 1.
The numbers 0, 1, 2, 3, ... .