 11.3.1: In Exercises 18, find (a) (b) (c) (d) and (e) u (2v)u 3, 4, v 2, 3
 11.3.2: In Exercises 18, find (a) (b) (c) (d) and (e) u (2v)
 11.3.3: In Exercises 18, find (a) (b) (c) (d) and (e) u (2v)u 5, 1, v 3, 2
 11.3.4: In Exercises 18, find (a) (b) (c) (d) and (e) u (2v)u 4, 8, v 6, 3
 11.3.5: In Exercises 18, find (a) (b) (c) (d) and (e) u (2v)u 2, 3, 4, v 0,...
 11.3.6: In Exercises 18, find (a) (b) (c) (d) and (e) u (2v)
 11.3.7: In Exercises 18, find (a) (b) (c) (d) and (e) u (2v)
 11.3.8: In Exercises 18, find (a) (b) (c) (d) and (e) u (2v)u 2i j 2kv i 3j 2k
 11.3.9: In Exercises 9 and 10, find u.v
 11.3.10: In Exercises 9 and 10, find u.v
 11.3.11: In Exercises 1118, find the angle between the vectors.u 1, 1, v 2, 2
 11.3.12: In Exercises 1118, find the angle between the vectors.u 3, 1, v 2, 1
 11.3.13: In Exercises 1118, find the angle between the vectors.
 11.3.14: In Exercises 1118, find the angle between the vectors.v cos34 i sin...
 11.3.15: In Exercises 1118, find the angle between the vectors.
 11.3.16: In Exercises 1118, find the angle between the vectors.
 11.3.17: In Exercises 1118, find the angle between the vectors.
 11.3.18: In Exercises 1118, find the angle between the vectors.
 11.3.19: In Exercises 1926, determine whether u and v are orthogonal, parall...
 11.3.20: In Exercises 1926, determine whether u and v are orthogonal, parall...
 11.3.21: In Exercises 1926, determine whether u and v are orthogonal, parall...
 11.3.22: In Exercises 1926, determine whether u and v are orthogonal, parall...
 11.3.23: In Exercises 1926, determine whether u and v are orthogonal, parall...
 11.3.24: In Exercises 1926, determine whether u and v are orthogonal, parall...
 11.3.25: In Exercises 1926, determine whether u and v are orthogonal, parall...
 11.3.26: In Exercises 1926, determine whether u and v are orthogonal, parall...
 11.3.27: In Exercises 2730, the vertices of a triangle are given. Determine ...
 11.3.28: In Exercises 2730, the vertices of a triangle are given. Determine ...
 11.3.29: In Exercises 2730, the vertices of a triangle are given. Determine ...
 11.3.30: In Exercises 2730, the vertices of a triangle are given. Determine ...
 11.3.31: In Exercises 3134, find the direction cosines of u and demonstrate ...
 11.3.32: In Exercises 3134, find the direction cosines of u and demonstrate ...
 11.3.33: In Exercises 3134, find the direction cosines of u and demonstrate ...
 11.3.34: In Exercises 3134, find the direction cosines of u and demonstrate ...
 11.3.35: In Exercises 3538, find the direction angles of the vector.u 3i 2j ...
 11.3.36: In Exercises 3538, find the direction angles of the vector.
 11.3.37: In Exercises 3538, find the direction angles of the vector.
 11.3.38: In Exercises 3538, find the direction angles of the vector.u 2, 6, 1
 11.3.39: In Exercises 39 and 40, use a graphing utility to find the magnitud...
 11.3.40: In Exercises 39 and 40, use a graphing utility to find the magnitud...
 11.3.41: LoadSupporting Cables A load is supported by three cables, as show...
 11.3.42: LoadSupporting Cables The tension in the cable in Exercise 41 is 2...
 11.3.43: In Exercises 4346, find the component of u that is orthogonal to v,...
 11.3.44: In Exercises 4346, find the component of u that is orthogonal to v,...
 11.3.45: In Exercises 4346, find the component of u that is orthogonal to v,...
 11.3.46: In Exercises 4346, find the component of u that is orthogonal to v,...
 11.3.47: In Exercises 4750, (a) find the projection of u onto v, and (b) fin...
 11.3.48: In Exercises 4750, (a) find the projection of u onto v, and (b) fin...
 11.3.49: In Exercises 4750, (a) find the projection of u onto v, and (b) fin...
 11.3.50: In Exercises 4750, (a) find the projection of u onto v, and (b) fin...
 11.3.51: Define the dot product of vectors and v
 11.3.52: State the definition of orthogonal vectors. If vectors are neither ...
 11.3.53: What is known about the angle between two nonzero vectors and if u ...
 11.3.54: Determine which of the following are defined for nonzero vectors an...
 11.3.55: Describe direction cosines and direction angles of a vector v
 11.3.56: Give a geometric description of the projection of onto v
 11.3.57: What can be said about the vectors and if (a) the projection of ont...
 11.3.58: If the projection of onto has the same magnitude as the projection ...
 11.3.59: Revenue The vector gives the numbers of hamburgers, chicken sandwic...
 11.3.60: Revenue Repeat Exercise 59 after increasing prices by 4%. Identify ...
 11.3.61: Programming Given vectors and in component form, write a program fo...
 11.3.62: Programming Use the program you wrote in Exercise 61 to find the an...
 11.3.63: Programming Given vectors and in component form, write a program fo...
 11.3.64: Programming Use the program you wrote in Exercise 63 to find the pr...
 11.3.65: Think About It In Exercises 65 and 66, use the figure to determine ...
 11.3.66: Think About It In Exercises 65 and 66, use the figure to determine ...
 11.3.67: In Exercises 6770, find two vectors in opposite directions that are...
 11.3.68: In Exercises 6770, find two vectors in opposite directions that are...
 11.3.69: In Exercises 6770, find two vectors in opposite directions that are...
 11.3.70: In Exercises 6770, find two vectors in opposite directions that are...
 11.3.71: Braking Load A 48,000pound truck is parked on a slope (see figure)...
 11.3.72: LoadSupporting Cables Find the magnitude of the projection of the ...
 11.3.73: Work An object is pulled 10 feet across a floor, using a force of 8...
 11.3.74: Work A toy wagon is pulled by exerting a force of 25 pounds on a ha...
 11.3.75: True or False? In Exercises 75 and 76, determine whether the statem...
 11.3.76: True or False? In Exercises 75 and 76, determine whether the statem...
 11.3.77: Find the angle between a cubes diagonal and one of its edges
 11.3.78: Find the angle between the diagonal of a cube and the diagonal of o...
 11.3.79: In Exercises 7982, (a) find the unit tangent vectors to each curve ...
 11.3.80: In Exercises 7982, (a) find the unit tangent vectors to each curve ...
 11.3.81: In Exercises 7982, (a) find the unit tangent vectors to each curve ...
 11.3.82: In Exercises 7982, (a) find the unit tangent vectors to each curve ...
 11.3.83: Use vectors to prove that the diagonals of a rhombus are perpendicular
 11.3.84: Use vectors to prove that a parallelogram is a rectangle if and onl...
 11.3.85: Bond Angle Consider a regular tetrahedron with vertices and where i...
 11.3.86: Consider the vectors and where Find the dot product of the vectors ...
 11.3.87: Prove that u v2 u 2 v2 2u v.c
 11.3.88: Prove the CauchySchwarz Inequality u v u v.
 11.3.89: Prove the triangle inequality u v u v.
 11.3.90: Prove Theorem 11.6.
Solutions for Chapter 11.3: The Dot Product of Two Vectors
Full solutions for Calculus: Early Transcendental Functions  4th Edition
ISBN: 9780618606245
Solutions for Chapter 11.3: The Dot Product of Two Vectors
Get Full SolutionsCalculus: Early Transcendental Functions was written by and is associated to the ISBN: 9780618606245. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 11.3: The Dot Product of Two Vectors includes 90 full stepbystep solutions. Since 90 problems in chapter 11.3: The Dot Product of Two Vectors have been answered, more than 41565 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Calculus: Early Transcendental Functions , edition: 4.

Aphelion
The farthest point from the Sun in a planet’s orbit

Arccotangent function
See Inverse cotangent function.

Arithmetic sequence
A sequence {an} in which an = an1 + d for every integer n ? 2 . The number d is the common difference.

Binomial coefficients
The numbers in Pascal’s triangle: nCr = anrb = n!r!1n  r2!

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

Convenience sample
A sample that sacrifices randomness for convenience

Cycloid
The graph of the parametric equations

Firstdegree equation in x , y, and z
An equation that can be written in the form.

Identity
An equation that is always true throughout its domain.

Identity properties
a + 0 = a, a ? 1 = a

Instantaneous velocity
The instantaneous rate of change of a position function with respect to time, p. 737.

Length of a vector
See Magnitude of a vector.

Linear system
A system of linear equations

NDER ƒ(a)
See Numerical derivative of ƒ at x = a.

Normal distribution
A distribution of data shaped like the normal curve.

Number line graph of a linear inequality
The graph of the solutions of a linear inequality (in x) on a number line

Quartile
The first quartile is the median of the lower half of a set of data, the second quartile is the median, and the third quartile is the median of the upper half of the data.

Reexpression of data
A transformation of a data set.

Reference angle
See Reference triangle

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