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# Solutions for Chapter 10: Vectors and the Geometry of Space ## Full solutions for Essential Calculus | 2nd Edition

ISBN: 9781133112297 Solutions for Chapter 10: Vectors and the Geometry of Space

Solutions for Chapter 10
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##### ISBN: 9781133112297

Summary of Chapter 10: Vectors and the Geometry of Space

In this chapter we will see that vectors provide particularly simple descriptions of lines, planes, and curves. We will also use vector-valued functions to describe the motion of objects through space. In particular, we will use them to derive Kepler’s laws of planetary motion.

Essential Calculus was written by and is associated to the ISBN: 9781133112297. Chapter 10: Vectors and the Geometry of Space includes 57 full step-by-step solutions. This textbook survival guide was created for the textbook: Essential Calculus, edition: 2. Since 57 problems in chapter 10: Vectors and the Geometry of Space have been answered, more than 26592 students have viewed full step-by-step solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions.

Key Calculus Terms and definitions covered in this textbook
• Ambiguous case

The case in which two sides and a nonincluded angle can determine two different triangles

• Anchor

See Mathematical induction.

• Arithmetic sequence

A sequence {an} in which an = an-1 + d for every integer n ? 2 . The number d is the common difference.

• Blocking

A feature of some experimental designs that controls for potential differences between subject groups by applying treatments randomly within homogeneous blocks of subjects

• Causation

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

• Combinations of n objects taken r at a time

There are nCr = n! r!1n - r2! such combinations,

• Convenience sample

A sample that sacrifices randomness for convenience

• Divisor of a polynomial

See Division algorithm for polynomials.

• Explanatory variable

A variable that affects a response variable.

• Graph of parametric equations

The set of all points in the coordinate plane corresponding to the ordered pairs determined by the parametric equations.

• Imaginary axis

See Complex plane.

• Implicitly defined function

A function that is a subset of a relation defined by an equation in x and y.

• Length of an arrow

See Magnitude of an arrow.

• Linear regression equation

Equation of a linear regression line

• Obtuse triangle

A triangle in which one angle is greater than 90°.

• Polynomial interpolation

The process of fitting a polynomial of degree n to (n + 1) points.

• Positive angle

Angle generated by a counterclockwise rotation.

• Root of a number

See Principal nth root.

• Triangular number

A number that is a sum of the arithmetic series 1 + 2 + 3 + ... + n for some natural number n.

• Zero factor property

If ab = 0 , then either a = 0 or b = 0.