×
Log in to StudySoup
Get Full Access to Calculus - Textbook Survival Guide
Join StudySoup for FREE
Get Full Access to Calculus - Textbook Survival Guide

Solutions for Chapter 12: Vectors and the Geometry of Space

Thomas' Calculus Early Transcendentals | 12th Edition | ISBN: 9780321588760 | Authors: George B. Thomas

Full solutions for Thomas' Calculus Early Transcendentals | 12th Edition

ISBN: 9780321588760

Thomas' Calculus Early Transcendentals | 12th Edition | ISBN: 9780321588760 | Authors: George B. Thomas

Solutions for Chapter 12: Vectors and the Geometry of Space

Solutions for Chapter 12
4 5 0 397 Reviews
20
2
Textbook: Thomas' Calculus Early Transcendentals
Edition: 12
Author: George B. Thomas
ISBN: 9780321588760

Thomas' Calculus Early Transcendentals was written by and is associated to the ISBN: 9780321588760. This textbook survival guide was created for the textbook: Thomas' Calculus Early Transcendentals, edition: 12. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 12: Vectors and the Geometry of Space includes 76 full step-by-step solutions. Since 76 problems in chapter 12: Vectors and the Geometry of Space have been answered, more than 7322 students have viewed full step-by-step solutions from this chapter.

Key Calculus Terms and definitions covered in this textbook
  • Arccotangent function

    See Inverse cotangent function.

  • Associative properties

    a + (b + c) = (a + b) + c, a(bc) = (ab)c.

  • Circular functions

    Trigonometric functions when applied to real numbers are circular functions

  • Complex conjugates

    Complex numbers a + bi and a - bi

  • Conjugate axis of a hyperbola

    The line segment of length 2b that is perpendicular to the focal axis and has the center of the hyperbola as its midpoint

  • De Moivre’s theorem

    (r(cos ? + i sin ?))n = r n (cos n? + i sin n?)

  • Degree

    Unit of measurement (represented by the symbol ) for angles or arcs, equal to 1/360 of a complete revolution

  • Difference identity

    An identity involving a trigonometric function of u - v

  • Direction of an arrow

    The angle the arrow makes with the positive x-axis

  • Distance (in a coordinate plane)

    The distance d(P, Q) between P(x, y) and Q(x, y) d(P, Q) = 2(x 1 - x 2)2 + (y1 - y2)2

  • Domain of validity of an identity

    The set of values of the variable for which both sides of the identity are defined

  • Gaussian elimination

    A method of solving a system of n linear equations in n unknowns.

  • Polar distance formula

    The distance between the points with polar coordinates (r1, ?1 ) and (r2, ?2 ) = 2r 12 + r 22 - 2r1r2 cos 1?1 - ?22

  • Quadratic equation in x

    An equation that can be written in the form ax 2 + bx + c = 01a ? 02

  • Root of a number

    See Principal nth root.

  • Semiperimeter of a triangle

    One-half of the sum of the lengths of the sides of a triangle.

  • Tangent

    The function y = tan x

  • Transformation

    A function that maps real numbers to real numbers.

  • Vector equation for a line in space

    The line through P0(x 0, y0, z0) in the direction of the nonzero vector V = <a, b, c> has vector equation r = r0 + tv , where r = <x,y,z>.

  • Zero factorial

    See n factorial.

×
Log in to StudySoup
Get Full Access to Calculus - Textbook Survival Guide
Join StudySoup for FREE
Get Full Access to Calculus - Textbook Survival Guide
×
Reset your password