 6.7.1: In Exercises 1 8, use the given vectors to find v.w and v.v
 6.7.2: In Exercises 1 8, use the given vectors to find v.w and v.v
 6.7.3: In Exercises 1 8, use the given vectors to find v.w and v.v
 6.7.4: In Exercises 1 8, use the given vectors to find v.w and v.v
 6.7.5: In Exercises 1 8, use the given vectors to find v.w and v.v
 6.7.6: In Exercises 1 8, use the given vectors to find v.w and v.v
 6.7.7: In Exercises 1 8, use the given vectors to find v.w and v.v
 6.7.8: In Exercises 1 8, use the given vectors to find v.w and v.v
 6.7.9: In Exercises 9 16, let u = 2i  j, v = 3i + j, and w = i + 4j.
 6.7.10: In Exercises 9 16, let u = 2i  j, v = 3i + j, and w = i + 4j.
 6.7.11: In Exercises 9 16, let u = 2i  j, v = 3i + j, and w = i + 4j.
 6.7.12: In Exercises 9 16, let u = 2i  j, v = 3i + j, and w = i + 4j.
 6.7.13: In Exercises 9 16, let u = 2i  j, v = 3i + j, and w = i + 4j.
 6.7.14: In Exercises 9 16, let u = 2i  j, v = 3i + j, and w = i + 4j.
 6.7.15: In Exercises 9 16, let u = 2i  j, v = 3i + j, and w = i + 4j.
 6.7.16: In Exercises 9 16, let u = 2i  j, v = 3i + j, and w = i + 4j.
 6.7.17: In Exercises 17 22, find the angle between v and w. Round to the ne...
 6.7.18: In Exercises 17 22, find the angle between v and w. Round to the ne...
 6.7.19: In Exercises 17 22, find the angle between v and w. Round to the ne...
 6.7.20: In Exercises 17 22, find the angle between v and w. Round to the ne...
 6.7.21: In Exercises 17 22, find the angle between v and w. Round to the ne...
 6.7.22: In Exercises 17 22, find the angle between v and w. Round to the ne...
 6.7.23: In Exercises 23 32, use the dot product to determine whether v and ...
 6.7.24: In Exercises 23 32, use the dot product to determine whether v and ...
 6.7.25: In Exercises 23 32, use the dot product to determine whether v and ...
 6.7.26: In Exercises 23 32, use the dot product to determine whether v and ...
 6.7.27: In Exercises 23 32, use the dot product to determine whether v and ...
 6.7.28: In Exercises 23 32, use the dot product to determine whether v and ...
 6.7.29: In Exercises 23 32, use the dot product to determine whether v and ...
 6.7.30: In Exercises 23 32, use the dot product to determine whether v and ...
 6.7.31: In Exercises 23 32, use the dot product to determine whether v and ...
 6.7.32: In Exercises 23 32, use the dot product to determine whether v and ...
 6.7.33: In Exercises 33 38, find Then decompose v into two vectors, and whe...
 6.7.34: In Exercises 33 38, find Then decompose v into two vectors, and whe...
 6.7.35: In Exercises 33 38, find Then decompose v into two vectors, and whe...
 6.7.36: In Exercises 33 38, find Then decompose v into two vectors, and whe...
 6.7.37: In Exercises 33 38, find Then decompose v into two vectors, and whe...
 6.7.38: In Exercises 33 38, find Then decompose v into two vectors, and whe...
 6.7.39: In Exercises 39 42, let u = i + j, v = 3i  2j, and w = 5j Find e...
 6.7.40: In Exercises 39 42, let u = i + j, v = 3i  2j, and w = 5j Find e...
 6.7.41: In Exercises 39 42, let u = i + j, v = 3i  2j, and w = 5j Find e...
 6.7.42: In Exercises 39 42, let u = i + j, v = 3i  2j, and w = 5j Find e...
 6.7.43: In Exercises 43 44, find the angle, in degrees, between v and w.
 6.7.44: In Exercises 43 44, find the angle, in degrees, between v and w.
 6.7.45: n Exercises 45 50, determine whether v and w are parallel, orthogon...
 6.7.46: n Exercises 45 50, determine whether v and w are parallel, orthogon...
 6.7.47: n Exercises 45 50, determine whether v and w are parallel, orthogon...
 6.7.48: n Exercises 45 50, determine whether v and w are parallel, orthogon...
 6.7.49: n Exercises 45 50, determine whether v and w are parallel, orthogon...
 6.7.50: n Exercises 45 50, determine whether v and w are parallel, orthogon...
 6.7.51: The components of represent the respective number of gallons of reg...
 6.7.52: The components of represent the respective number of oneday and th...
 6.7.53: Find the work done in pushing a car along a level road from point t...
 6.7.54: Find the work done when a crane lifts a 6000pound boulder through ...
 6.7.55: A wagon is pulled along level ground by exerting a force of 40 poun...
 6.7.56: A wagon is pulled along level ground by exerting a force of 25 poun...
 6.7.57: A force of 60 pounds on a rope is used to pull a box up a ramp incl...
 6.7.58: A force of 80 pounds on a rope is used to pull a box up a ramp incl...
 6.7.59: A force is given by the vector The force moves an object along a st...
 6.7.60: A force is given by the vector The force moves an object along a st...
 6.7.61: A force of 4 pounds acts in the direction of 50 to the horizontal. ...
 6.7.62: A force of 6 pounds acts in the direction of 40 to the horizontal. ...
 6.7.63: Refer to Figure 6.69 on page 716. Suppose that the boat weighs 700 ...
 6.7.64: Refer to Figure 6.69 on page 716. Suppose that the boat weighs 650 ...
 6.7.65: Explain how to find the dot product of two vectors
 6.7.66: Using words and no symbols, describe how to find the dot product of...
 6.7.67: Describe how to find the angle between two vectors.
 6.7.68: What are parallel vectors?
 6.7.69: What are orthogonal vectors?
 6.7.70: How do you determine if two vectors are orthogonal?
 6.7.71: Draw two vectors, v and w, with the same initial point. Show the ve...
 6.7.72: How do you determine the work done by a force F in moving an object...
 6.7.73: A weightlifter is holding a barbell perfectly still above his head,...
 6.7.74: Describe one way in which the everyday use of the word work is diff...
 6.7.75: Although I expected vector operations to produce another vector, th...
 6.7.76: I ve noticed that whenever the dot product is negative, the angle b...
 6.7.77: I m working with a unit vector, so its dot product with itself must...
 6.7.78: The weightlifter does more work in raising 300 kilograms above her ...
 6.7.79: In Exercises 79 81, use the vectors u = a1i + b1j, v = a2i + b2j, a...
 6.7.80: In Exercises 79 81, use the vectors u = a1i + b1j, v = a2i + b2j, a...
 6.7.81: In Exercises 79 81, use the vectors u = a1i + b1j, v = a2i + b2j, a...
 6.7.82: If v = 2i + 5jfind a vector orthogonal to v
 6.7.83: Find a value of so that and are orthogonal.
 6.7.84: Prove that the projection of v onto i is
 6.7.85: Find two vectors v and w such that the projection of v onto w is v
 6.7.86: Group members should research and present a report on unusual and i...
 6.7.87: a. Does satisfy b. Does satisfy 14, 12 x  2y = 6? 14, 12 x + 2y ...
 6.7.88: Graph and in the same rectangular coordinate system. At what point ...
 6.7.89: Solve: 512x  32  4x = 9.
Solutions for Chapter 6.7: The Dot Product
Full solutions for Precalculus  4th Edition
ISBN: 9780321559845
Solutions for Chapter 6.7: The Dot Product
Get Full SolutionsChapter 6.7: The Dot Product includes 89 full stepbystep solutions. Since 89 problems in chapter 6.7: The Dot Product have been answered, more than 107663 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Precalculus, edition: 4. This expansive textbook survival guide covers the following chapters and their solutions. Precalculus was written by and is associated to the ISBN: 9780321559845.

Angle
Union of two rays with a common endpoint (the vertex). The beginning ray (the initial side) can be rotated about its endpoint to obtain the final position (the terminal side)

Components of a vector
See Component form of a vector.

Coordinate plane
See Cartesian coordinate system.

Cosine
The function y = cos x

Discriminant
For the equation ax 2 + bx + c, the expression b2  4ac; for the equation Ax2 + Bxy + Cy2 + Dx + Ey + F = 0, the expression B2  4AC

Graph of a function ƒ
The set of all points in the coordinate plane corresponding to the pairs (x, ƒ(x)) for x in the domain of ƒ.

Horizontal asymptote
The line is a horizontal asymptote of the graph of a function ƒ if lim x: q ƒ(x) = or lim x: q ƒ(x) = b

Horizontal line
y = b.

Implied domain
The domain of a function’s algebraic expression.

Inverse composition rule
The composition of a onetoone function with its inverse results in the identity function.

Leaf
The final digit of a number in a stemplot.

Natural logarithmic regression
A procedure for fitting a logarithmic curve to a set of data.

Positive angle
Angle generated by a counterclockwise rotation.

Product rule of logarithms
ogb 1RS2 = logb R + logb S, R > 0, S > 0,

Solve algebraically
Use an algebraic method, including paper and pencil manipulation and obvious mental work, with no calculator or grapher use. When appropriate, the final exact solution may be approximated by a calculator

Symmetric about the origin
A graph in which (x, y) is on the the graph whenever (x, y) is; or a graph in which (r, ?) or (r, ? + ?) is on the graph whenever (r, ?) is

Symmetric difference quotient of ƒ at a
ƒ(x + h)  ƒ(x  h) 2h

Variable
A letter that represents an unspecified number.

Vertical stretch or shrink
See Stretch, Shrink.

xzplane
The points x, 0, z in Cartesian space.