 13.4.1: In Exercises 17, use the algebraic definition to find v w .v = k,w = j
 13.4.2: In Exercises 17, use the algebraic definition to find v w .v = i , ...
 13.4.3: In Exercises 17, use the algebraic definition to find v w .v =i + k...
 13.4.4: In Exercises 17, use the algebraic definition to find v w .v =i +j ...
 13.4.5: In Exercises 17, use the algebraic definition to find v w .v = 2i 3...
 13.4.6: In Exercises 17, use the algebraic definition to find v w .v = 2i j...
 13.4.7: In Exercises 17, use the algebraic definition to find v w .v = 3i +...
 13.4.8: Use the geometric definition in Exercises 89 to find:2i (i +j )
 13.4.9: Use the geometric definition in Exercises 89 to find:(i +j ) (i j )
 13.4.10: In Exercises 1011, use the properties on page 746 to find:(i +j ) ij
 13.4.11: In Exercises 1011, use the properties on page 746 to find:(i +j ) (...
 13.4.12: For a = 3i +j k andb =i 4j + 2k , find a band check that it is perp...
 13.4.13: If v = 3i 2j + 4k and w = i + 2j k , findv w and w v . What is the ...
 13.4.14: In Exercises 1415, find an equation for the plane through the point...
 13.4.15: In Exercises 1415, find an equation for the plane through the point...
 13.4.16: In Exercises 1619, find the volume of the parallelogram withedges a...
 13.4.17: In Exercises 1619, find the volume of the parallelogram withedges a...
 13.4.18: In Exercises 1619, find the volume of the parallelogram withedges a...
 13.4.19: In Exercises 1619, find the volume of the parallelogram withedges a...
 13.4.20: Find a vector parallel to the line of intersection of theplanes giv...
 13.4.21: Find the equation of the plane through the origin that isperpendicu...
 13.4.22: Find the equation of the plane through the point (4, 5, 6)and perpe...
 13.4.23: Find an equation for the plane through the origin containingthe poi...
 13.4.24: Find a vector parallel to the line of intersection of the twoplanes...
 13.4.25: Find a vector parallel to the intersection of the planes2x 3y + 5z ...
 13.4.26: Find the equation of the plane through the origin that isperpendicu...
 13.4.27: Find the equation of the plane through the point (4, 5, 6)that is p...
 13.4.28: Find the equation of a plane through the origin and perpendicularto...
 13.4.29: Given the points P = (1, 2, 3), Q = (3, 5, 7), andR = (2, 5, 3), fi...
 13.4.30: Let A = (1, 3, 0), B = (3, 2, 4), and C = (1, 1, 5).(a) Find an equ...
 13.4.31: If v and w are both parallel to the xyplane, what canyou conclude ...
 13.4.32: Suppose v w = 5 and v w  = 3, and the anglebetween v and w is ....
 13.4.33: If v w = 2i 3j + 5k , and v w = 3, find tan where is the angle betw...
 13.4.34: Suppose v w = 8 and v w = 12i 3j + 4k andthat the angle between v a...
 13.4.35: Why does a baseball curve? The baseball in Figure 13.42has velocity...
 13.4.36: The point P in Figure 13.43 has position vector v obtainedby rotati...
 13.4.37: The points P1 = (0, 0, 0), P2 = (2, 4, 2), P3 =(3, 0, 0), and P4 = ...
 13.4.38: Using the parallelogram in as a base, createa parallelopiped with s...
 13.4.39: Use the algebraic definition to check thata (b + c )=(a b )+(a c ).
 13.4.40: If v and w are nonzero vectors, use the geometric definition of t...
 13.4.41: Use a parallelepiped to show that a (b c )=(a b )cfor any vectors a...
 13.4.42: Show that a b 2 = a 2b 2 (a b )2
 13.4.43: If a +b + c = 0 , show thata b = b c = c a .Geometrically, what doe...
 13.4.44: If a = a1i + a2j + a3k , b = b1i + b2j + b3k andc = c1i + c2j + c3k...
 13.4.45: Use the fact thati i = 0 ,i j = k ,i k = j ,and so on, together wit...
 13.4.46: In this problem, we arrive at the algebraic definition forthe cross...
 13.4.47: For vectors a and b , let c = a (b a ).(a) Show that c lies in the ...
 13.4.48: Use the result of to show that the cross productdistributes over ad...
 13.4.49: Figure 13.44 shows the tetrahedron determined by threevectors a ,b ...
 13.4.50: In 5052, find the vector representing the area of asurface. The mag...
 13.4.51: In 5052, find the vector representing the area of asurface. The mag...
 13.4.52: In 5052, find the vector representing the area of asurface. The mag...
 13.4.53: This problem relates the area of a parallelogram S lyingin the plan...
 13.4.54: In 5455, explain what is wrong with the statement.There is only one...
 13.4.55: In 5455, explain what is wrong with the statement.u v = 0 when u an...
 13.4.56: In 5657, give an example of:A vector u whose cross product with v =...
 13.4.57: In 5657, give an example of:A vector v such that u v = 10, where u ...
 13.4.58: Are the statements in 5867 true or false? Give reasonsfor your answ...
 13.4.59: Are the statements in 5867 true or false? Give reasonsfor your answ...
 13.4.60: Are the statements in 5867 true or false? Give reasonsfor your answ...
 13.4.61: Are the statements in 5867 true or false? Give reasonsfor your answ...
 13.4.62: Are the statements in 5867 true or false? Give reasonsfor your answ...
 13.4.63: Are the statements in 5867 true or false? Give reasonsfor your answ...
 13.4.64: Are the statements in 5867 true or false? Give reasonsfor your answ...
 13.4.65: Are the statements in 5867 true or false? Give reasonsfor your answ...
 13.4.66: Are the statements in 5867 true or false? Give reasonsfor your answ...
 13.4.67: Are the statements in 5867 true or false? Give reasonsfor your answ...
Solutions for Chapter 13.4: THE CROSS PRODUCT
Full solutions for Calculus: Single and Multivariable  6th Edition
ISBN: 9780470888612
Solutions for Chapter 13.4: THE CROSS PRODUCT
Get Full SolutionsCalculus: Single and Multivariable was written by and is associated to the ISBN: 9780470888612. This textbook survival guide was created for the textbook: Calculus: Single and Multivariable , edition: 6. Since 67 problems in chapter 13.4: THE CROSS PRODUCT have been answered, more than 44964 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 13.4: THE CROSS PRODUCT includes 67 full stepbystep solutions.

Bias
A flaw in the design of a sampling process that systematically causes the sample to differ from the population with respect to the statistic being measured. Undercoverage bias results when the sample systematically excludes one or more segments of the population. Voluntary response bias results when a sample consists only of those who volunteer their responses. Response bias results when the sampling design intentionally or unintentionally influences the responses

Binomial theorem
A theorem that gives an expansion formula for (a + b)n

Circle graph
A circular graphical display of categorical data

Direction vector for a line
A vector in the direction of a line in threedimensional space

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

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

Imaginary part of a complex number
See Complex number.

Irrational zeros
Zeros of a function that are irrational numbers.

n factorial
For any positive integer n, n factorial is n! = n.(n  1) . (n  2) .... .3.2.1; zero factorial is 0! = 1

Nonsingular matrix
A square matrix with nonzero determinant

nth root of a complex number z
A complex number v such that vn = z

Ordinary annuity
An annuity in which deposits are made at the same time interest is posted.

Orthogonal vectors
Two vectors u and v with u x v = 0.

Period
See Periodic function.

Product of a scalar and a vector
The product of scalar k and vector u = 8u1, u29 1or u = 8u1, u2, u392 is k.u = 8ku1, ku291or k # u = 8ku1, ku2, ku392,

Sum of an infinite geometric series
Sn = a 1  r , r 6 1

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

Unit circle
A circle with radius 1 centered at the origin.

Vertical line test
A test for determining whether a graph is a function.

Window dimensions
The restrictions on x and y that specify a viewing window. See Viewing window.