 11.3.1: Express the dot product of u and v in terms of their magnitudes and...
 11.3.2: Express the dot product of u and v in terms of the components of th...
 11.3.3: Compute 82, 3, 69 ~ 81, 8, 39.
 11.3.4: What is the dot product of two orthogonal vectors?
 11.3.5: Explain how to find the angle between two nonzero vectors.
 11.3.6: Use a sketch to illustrate the projection of u onto v.
 11.3.7: Use a sketch to illustrate the scalar component of u in the directi...
 11.3.8: Explain how the work done by a force in moving an object is compute...
 11.3.9: 912. Dot product from the definition Consider the following vectors...
 11.3.10: 912. Dot product from the definition Consider the following vectors...
 11.3.11: 912. Dot product from the definition Consider the following vectors...
 11.3.12: 912. Dot product from the definition Consider the following vectors...
 11.3.13: Dot product from the definition Compute u ~ v if u and v are unit v...
 11.3.14: Dot product from the definition Compute u ~ v if u is a unit vector...
 11.3.15: 1524. Dot products and angles Compute the dot product of the vector...
 11.3.16: 1524. Dot products and angles Compute the dot product of the vector...
 11.3.17: 1524. Dot products and angles Compute the dot product of the vector...
 11.3.18: 1524. Dot products and angles Compute the dot product of the vector...
 11.3.19: 1524. Dot products and angles Compute the dot product of the vector...
 11.3.20: 1524. Dot products and angles Compute the dot product of the vector...
 11.3.21: 1524. Dot products and angles Compute the dot product of the vector...
 11.3.22: 1524. Dot products and angles Compute the dot product of the vector...
 11.3.23: 1524. Dot products and angles Compute the dot product of the vector...
 11.3.24: 1524. Dot products and angles Compute the dot product of the vector...
 11.3.25: 2528. Sketching orthogonal projections Find projvu and scalvu by in...
 11.3.26: 2528. Sketching orthogonal projections Find projvu and scalvu by in...
 11.3.27: 2528. Sketching orthogonal projections Find projvu and scalvu by in...
 11.3.28: 2528. Sketching orthogonal projections Find projvu and scalvu by in...
 11.3.29: 2936. Calculating orthogonal projections For the given vectors u an...
 11.3.30: 2936. Calculating orthogonal projections For the given vectors u an...
 11.3.31: 2936. Calculating orthogonal projections For the given vectors u an...
 11.3.32: 2936. Calculating orthogonal projections For the given vectors u an...
 11.3.33: 2936. Calculating orthogonal projections For the given vectors u an...
 11.3.34: 2936. Calculating orthogonal projections For the given vectors u an...
 11.3.35: 2936. Calculating orthogonal projections For the given vectors u an...
 11.3.36: 2936. Calculating orthogonal projections For the given vectors u an...
 11.3.37: 3742. Computing work Calculate the work done in the following situa...
 11.3.38: 3742. Computing work Calculate the work done in the following situa...
 11.3.39: 3742. Computing work Calculate the work done in the following situa...
 11.3.40: 3742. Computing work Calculate the work done in the following situa...
 11.3.41: 3742. Computing work Calculate the work done in the following situa...
 11.3.42: 3742. Computing work Calculate the work done in the following situa...
 11.3.43: 4346. Parallel and normal forces Find the components of the v ertic...
 11.3.44: 4346. Parallel and normal forces Find the components of the v ertic...
 11.3.45: 4346. Parallel and normal forces Find the components of the v ertic...
 11.3.46: 4346. Parallel and normal forces Find the components of the v ertic...
 11.3.47: Explain why or why not Determine whether the following statements a...
 11.3.48: Find all unit vectors orthogonal to v = 83, 4, 09. 4
 11.3.49: Find all vectors 81, a, b9 orthogonal to 84, 8, 29. 5
 11.3.50: Describe all unit vectors orthogonal to v = i + j + k. 5
 11.3.51: Find three mutually orthogonal unit vectors in _3 besides {i, {j, a...
 11.3.52: Find two vectors that are orthogonal to 80, 1, 19 and to each other. 5
 11.3.53: Equal angles Consider the set of all unit position vectors u in _3 ...
 11.3.54: Find another vector that has the same projection onto v = 81, 19 as...
 11.3.55: Let v = 81, 19. Give a description of the position vectors u such t...
 11.3.56: Find another vector that has the same projection onto v = 81, 1, 19...
 11.3.57: Let v = 80, 0, 19. Give a description of all position vectors u suc...
 11.3.58: 5861. Decomposing vectors For the following vectors u and v, expres...
 11.3.59: 5861. Decomposing vectors For the following vectors u and v, expres...
 11.3.60: 5861. Decomposing vectors For the following vectors u and v, expres...
 11.3.61: 5861. Decomposing vectors For the following vectors u and v, expres...
 11.3.62: 6265. Distance between a point and a line Carry out the following s...
 11.3.63: 6265. Distance between a point and a line Carry out the following s...
 11.3.64: 6265. Distance between a point and a line Carry out the following s...
 11.3.65: 6265. Distance between a point and a line Carry out the following s...
 11.3.66: 6668. Orthogonal unit vectors in 2 Consider the vectors I = 81>12, ...
 11.3.67: 6668. Orthogonal unit vectors in 2 Consider the vectors I = 81>12, ...
 11.3.68: 6668. Orthogonal unit vectors in 2 Consider the vectors I = 81>12, ...
 11.3.69: Orthogonal unit vectors in _3 Consider the vectors I = 81>2, 1>2, 1...
 11.3.70: 7071. Angles of a triangle For the given points P, Q, and R, find t...
 11.3.71: 7071. Angles of a triangle For the given points P, Q, and R, find t...
 11.3.72: Flow through a circle Suppose water flows in a thin sheet over the ...
 11.3.73: Heat flux Let D be a solid heatconducting cube formed by the plane...
 11.3.74: Hexagonal circle packing The German mathematician Gauss proved that...
 11.3.75: Hexagonal sphere packing Imagine three unit spheres (radius equal t...
 11.3.76: 7680. Properties of dot products Let u = 8u1, u2, u39 , v = 8v1, v2...
 11.3.77: 7680. Properties of dot products Let u = 8u1, u2, u39 , v = 8v1, v2...
 11.3.78: 7680. Properties of dot products Let u = 8u1, u2, u39 , v = 8v1, v2...
 11.3.79: 7680. Properties of dot products Let u = 8u1, u2, u39 , v = 8v1, v2...
 11.3.80: 7680. Properties of dot products Let u = 8u1, u2, u39 , v = 8v1, v2...
 11.3.81: Prove or disprove For fixed values of a, b, c, and d, the value of ...
 11.3.82: Orthogonal lines Recall that two lines y = mx + b and y = nx + c ar...
 11.3.83: Direction angles and cosines Let v = 8a, b, c9 and let a, b, and g ...
 11.3.84: What conditions on u and v lead to equality in the Cauchy Schwarz I...
 11.3.85: Verify that the CauchySchwarz Inequality holds for u = 83, 5, 69 a...
 11.3.86: Geometricarithmetic mean Use the vectors u = 81a, 1b9 and v = 81b,...
 11.3.87: Triangle Inequality Consider the vectors u, v, and u + v (in any nu...
 11.3.88: Algebra inequality Show that 1u1 + u2 + u322 31u1 2 + u2 2 + u3 2 2...
 11.3.89: Diagonals of a parallelogram Consider the parallelogram with adjace...
 11.3.90: Distance between a point and a line in the plane Use projections to...
Solutions for Chapter 11.3: Calculus: Early Transcendentals 2nd Edition
Full solutions for Calculus: Early Transcendentals  2nd Edition
ISBN: 9780321947345
Solutions for Chapter 11.3
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 2. Chapter 11.3 includes 90 full stepbystep solutions. Since 90 problems in chapter 11.3 have been answered, more than 54573 students have viewed full stepbystep solutions from this chapter. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321947345.

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)

Bar chart
A rectangular graphical display of categorical data.

Bounded above
A function is bounded above if there is a number B such that ƒ(x) ? B for all x in the domain of ƒ.

Circle graph
A circular graphical display of categorical data

Closed interval
An interval that includes its endpoints

Combinations of n objects taken r at a time
There are nCr = n! r!1n  r2! such combinations,

Distributive property
a(b + c) = ab + ac and related properties

equation of a quadratic function
ƒ(x) = ax 2 + bx + c(a ? 0)

Equilibrium point
A point where the supply curve and demand curve intersect. The corresponding price is the equilibrium price.

Event
A subset of a sample space.

Expanded form of a series
A series written explicitly as a sum of terms (not in summation notation).

Horizontal translation
A shift of a graph to the left or right.

Index of summation
See Summation notation.

Line of symmetry
A line over which a graph is the mirror image of itself

Negative numbers
Real numbers shown to the left of the origin on a number line.

Plane in Cartesian space
The graph of Ax + By + Cz + D = 0, where A, B, and C are not all zero.

Variable
A letter that represents an unspecified number.

Wrapping function
The function that associates points on the unit circle with points on the real number line

xyplane
The points x, y, 0 in Cartesian space.

yintercept
A point that lies on both the graph and the yaxis.