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# Solutions for Chapter 12.3: Dot Product and the Angle Between Two Vectors ## Full solutions for Calculus: Early Transcendentals | 3rd Edition

ISBN: 9781464114885 Solutions for Chapter 12.3: Dot Product and the Angle Between Two Vectors

Solutions for Chapter 12.3
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##### ISBN: 9781464114885

This textbook survival guide was created for the textbook: Calculus: Early Transcendentals , edition: 3. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9781464114885. Chapter 12.3: Dot Product and the Angle Between Two Vectors includes 99 full step-by-step solutions. Since 99 problems in chapter 12.3: Dot Product and the Angle Between Two Vectors have been answered, more than 44628 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
• Bounded interval

An interval that has finite length (does not extend to ? or -?)

• Combination

An arrangement of elements of a set, in which order is not important

• Coordinate(s) of a point

The number associated with a point on a number line, or the ordered pair associated with a point in the Cartesian coordinate plane, or the ordered triple associated with a point in the Cartesian three-dimensional space

• 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

• End behavior

The behavior of a graph of a function as.

• equation of a hyperbola

(x - h)2 a2 - (y - k)2 b2 = 1 or (y - k)2 a2 - (x - h)2 b2 = 1

• Fibonacci numbers

The terms of the Fibonacci sequence.

• General form (of a line)

Ax + By + C = 0, where A and B are not both zero.

• Geometric series

A series whose terms form a geometric sequence.

• Line of travel

The path along which an object travels

• NINT (ƒ(x), x, a, b)

A calculator approximation to ?ab ƒ(x)dx

• Parabola

The graph of a quadratic function, or the set of points in a plane that are equidistant from a fixed point (the focus) and a fixed line (the directrix).

• Random numbers

Numbers that can be used by researchers to simulate randomness in scientific studies (they are usually obtained from lengthy tables of decimal digits that have been generated by verifiably random natural phenomena).

• Right triangle

A triangle with a 90° angle.

• Solve a triangle

To find one or more unknown sides or angles of a triangle

• Stretch of factor c

A transformation of a graph obtained by multiplying all the x-coordinates (horizontal stretch) by the constant 1/c, or all of the y-coordinates (vertical stretch) of the points by a constant c, c, > 1.

• Supply curve

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

• Symmetric matrix

A matrix A = [aij] with the property aij = aji for all i and j

• Tangent line of ƒ at x = a

The line through (a, ƒ(a)) with slope ƒ'(a) provided ƒ'(a) exists.

• Zoom out

A procedure of a graphing utility used to view more of the coordinate plane (used, for example, to find theend behavior of a function).

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