 13.3.1: For Exercises 19, perform the following operations on thegiven 3di...
 13.3.2: For Exercises 19, perform the following operations on thegiven 3di...
 13.3.3: For Exercises 19, perform the following operations on thegiven 3di...
 13.3.4: For Exercises 19, perform the following operations on thegiven 3di...
 13.3.5: For Exercises 19, perform the following operations on thegiven 3di...
 13.3.6: For Exercises 19, perform the following operations on thegiven 3di...
 13.3.7: For Exercises 19, perform the following operations on thegiven 3di...
 13.3.8: For Exercises 19, perform the following operations on thegiven 3di...
 13.3.9: For Exercises 19, perform the following operations on thegiven 3di...
 13.3.10: In Exercises 1014, find a normal vector to the plane.2x + y z = 5
 13.3.11: In Exercises 1014, find a normal vector to the plane.2(x z) = 3(x + y)
 13.3.12: In Exercises 1014, find a normal vector to the plane.1.5x + 3.2y + ...
 13.3.13: In Exercises 1014, find a normal vector to the plane.z = 3x + 4y 7
 13.3.14: In Exercises 1014, find a normal vector to the plane.(x 1) = (1 )(y...
 13.3.15: In Exercises 1521, find an equation of a plane that satisfiesthe gi...
 13.3.16: In Exercises 1521, find an equation of a plane that satisfiesthe gi...
 13.3.17: In Exercises 1521, find an equation of a plane that satisfiesthe gi...
 13.3.18: In Exercises 1521, find an equation of a plane that satisfiesthe gi...
 13.3.19: In Exercises 1521, find an equation of a plane that satisfiesthe gi...
 13.3.20: In Exercises 1521, find an equation of a plane that satisfiesthe gi...
 13.3.21: In Exercises 1521, find an equation of a plane that satisfiesthe gi...
 13.3.22: In Exercises 2226, compute the angle between the vectors.i +j + k a...
 13.3.23: In Exercises 2226, compute the angle between the vectors.. i + k an...
 13.3.24: In Exercises 2226, compute the angle between the vectors.i +j k and...
 13.3.25: In Exercises 2226, compute the angle between the vectors.i +j andi ...
 13.3.26: In Exercises 2226, compute the angle between the vectors.i and 2i +...
 13.3.27: Give a unit vector(a) In the same direction as v = 2i + 3j .(b) Per...
 13.3.28: A plane has equation z = 5x 2y + 7.(a) Find a value of making the v...
 13.3.29: Consider the plane 5x y + 7z = 21.(a) Find a point on the xaxis on...
 13.3.30: (a) Find a vector perpendicular to the planez =2+3x y.(b) Find a ve...
 13.3.31: (a) Find a vector perpendicular to the planez = 2x + 3y.(b) Find a ...
 13.3.32: Match the planes in (a)(d) with one or more of the descriptionsin (...
 13.3.33: Which pairs (if any) of vectors from the following list(a) Are perp...
 13.3.34: List any vectors that are parallel to each other and anyvectors tha...
 13.3.35: (a) Give a vector that is parallel to, but not equal to,v = 4i + 3j...
 13.3.36: For what values of t are u = ti j + k and v =ti + tj 2k perpendicul...
 13.3.37: Let be the angle between v and w , with 0 < < /2.What is the effect...
 13.3.38: Write a = 3i + 2j 6k as the sum of two vectors, oneparallel, and on...
 13.3.39: Find angle BAC if A = (2, 2, 2), B = (4, 2, 1), andC = (2, 3, 1).
 13.3.40: The points (5, 0, 0), (0, 3, 0), and (0, 0, 2) form a triangle.Find...
 13.3.41: Let S be the triangle with vertices A = (2, 2, 2), B =(4, 2, 1), an...
 13.3.42: In 4247, given v = 3i + 4j and force vector F ,find:(a) The compone...
 13.3.43: In 4247, given v = 3i + 4j and force vector F ,find:(a) The compone...
 13.3.44: In 4247, given v = 3i + 4j and force vector F ,find:(a) The compone...
 13.3.45: In 4247, given v = 3i + 4j and force vector F ,find:(a) The compone...
 13.3.46: In 4247, given v = 3i + 4j and force vector F ,find:(a) The compone...
 13.3.47: In 4247, given v = 3i + 4j and force vector F ,find:(a) The compone...
 13.3.48: In 4851, the force on an object is F = 20j . Forvector v , find:(a)...
 13.3.49: In 4851, the force on an object is F = 20j . Forvector v , find:(a)...
 13.3.50: In 4851, the force on an object is F = 20j . Forvector v , find:(a)...
 13.3.51: In 4851, the force on an object is F = 20j . Forvector v , find:(a)...
 13.3.52: A basketball gymnasium is 25 meters high, 80 meterswide and 200 met...
 13.3.53: A 100meter dash is run on a track in the direction of thevector v ...
 13.3.54: An airplane is flying toward the southeast. Which ofthe following w...
 13.3.55: A canoe is moving with velocity v = 5i + 3j m/sec relativeto the wa...
 13.3.56: Find a vector that bisects the smaller of the two anglesformed by 3...
 13.3.57: Find the shortest distance between the planes 2x 5y +z = 10 and z =...
 13.3.58: A street vendor sells six items, with prices p1 dollarsper unit, p2...
 13.3.59: A course has four exams, weighted 10%, 15%, 25%,50%, respectively. ...
 13.3.60: A consumption vector of three goods is defined by x =(x1, x2, x3), ...
 13.3.61: What does Property 2 of the dot product in the box onpage 735 say g...
 13.3.62: Show that the vectors (b c )a (a c )b and c areperpendicular.
 13.3.63: Show why each of the properties of the dot product in thebox on pag...
 13.3.64: Show that if u and v are two vectors such thatu w = v wfor every ve...
 13.3.65: Show thatuu 2 vv 2 and uu v vu v have the same magnitude where u an...
 13.3.66: Figure 13.34 shows that, given three vectors u , v , andw , the sum...
 13.3.67: (a) Using the geometric definition of the dot product,show thatu (v...
 13.3.68: The Law of Cosines for a triangle with side lengths a, b,and c, and...
 13.3.69: Use 66 and 67 and the following steps toshow (without trigonometry)...
 13.3.70: For any vectors v and w , consider the following functionof t:q(t)=...
 13.3.71: In 7173, explain what is wrong with the statement.For any 3dimensi...
 13.3.72: In 7173, explain what is wrong with the statement.If u = i +j and v...
 13.3.73: In 7173, explain what is wrong with the statement.A normal vector f...
 13.3.74: In 7475, give an example of:A point (a, b) such that the displaceme...
 13.3.75: In 7475, give an example of:A linear function f(x, y) = mx + ny + c...
 13.3.76: Are the statements in 7685 true or false? Give reasonsfor your answ...
 13.3.77: Are the statements in 7685 true or false? Give reasonsfor your answ...
 13.3.78: Are the statements in 7685 true or false? Give reasonsfor your answ...
 13.3.79: Are the statements in 7685 true or false? Give reasonsfor your answ...
 13.3.80: Are the statements in 7685 true or false? Give reasonsfor your answ...
 13.3.81: Are the statements in 7685 true or false? Give reasonsfor your answ...
 13.3.82: Are the statements in 7685 true or false? Give reasonsfor your answ...
 13.3.83: Are the statements in 7685 true or false? Give reasonsfor your answ...
 13.3.84: Are the statements in 7685 true or false? Give reasonsfor your answ...
 13.3.85: Are the statements in 7685 true or false? Give reasonsfor your answ...
Solutions for Chapter 13.3: THE DOT PRODUCT
Full solutions for Calculus: Single and Multivariable  6th Edition
ISBN: 9780470888612
Solutions for Chapter 13.3: THE DOT PRODUCT
Get Full SolutionsSince 85 problems in chapter 13.3: THE DOT PRODUCT have been answered, more than 43302 students have viewed full stepbystep solutions from this chapter. Chapter 13.3: THE DOT PRODUCT includes 85 full stepbystep solutions. This textbook survival guide was created for the textbook: Calculus: Single and Multivariable , edition: 6. Calculus: Single and Multivariable was written by and is associated to the ISBN: 9780470888612. This expansive textbook survival guide covers the following chapters and their solutions.

Absolute value of a complex number
The absolute value of the complex number z = a + b is given by ?a2+b2; also, the length of the segment from the origin to z in the complex plane.

Addition property of inequality
If u < v , then u + w < v + w

Algebraic model
An equation that relates variable quantities associated with phenomena being studied

Factor
In algebra, a quantity being multiplied in a product. In statistics, a potential explanatory variable under study in an experiment, .

Factoring (a polynomial)
Writing a polynomial as a product of two or more polynomial factors.

Matrix, m x n
A rectangular array of m rows and n columns of real numbers

Multiplication property of equality
If u = v and w = z, then uw = vz

Multiplicative inverse of a complex number
The reciprocal of a + bi, or 1 a + bi = a a2 + b2 ba2 + b2 i

Nonsingular matrix
A square matrix with nonzero determinant

Piecewisedefined function
A function whose domain is divided into several parts with a different function rule applied to each part, p. 104.

Power rule of logarithms
logb Rc = c logb R, R 7 0.

Pythagorean
Theorem In a right triangle with sides a and b and hypotenuse c, c2 = a2 + b2

Quartic function
A degree 4 polynomial function.

Reciprocal of a real number
See Multiplicative inverse of a real number.

Remainder theorem
If a polynomial f(x) is divided by x  c , the remainder is ƒ(c)

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

Variable (in statistics)
A characteristic of individuals that is being identified or measured.

Vertex of a parabola
The point of intersection of a parabola and its line of symmetry.

yzplane
The points (0, y, z) in Cartesian space.

Zero of a function
A value in the domain of a function that makes the function value zero.