 11.4.1: In Exercises 16, find the cross product of the unit vectors and ske...
 11.4.2: In Exercises 16, find the cross product of the unit vectors and ske...
 11.4.3: In Exercises 16, find the cross product of the unit vectors and ske...
 11.4.4: In Exercises 16, find the cross product of the unit vectors and ske...
 11.4.5: In Exercises 16, find the cross product of the unit vectors and ske...
 11.4.6: In Exercises 16, find the cross product of the unit vectors and ske...
 11.4.7: In Exercises 710, find (a) (b) and
 11.4.8: In Exercises 710, find (a) (b) and
 11.4.9: In Exercises 710, find (a) (b) and
 11.4.10: In Exercises 710, find (a) (b) and
 11.4.11: In Exercises 1116, find and show that it is orthogonal to both u an...
 11.4.12: In Exercises 1116, find and show that it is orthogonal to both u an...
 11.4.13: In Exercises 1116, find and show that it is orthogonal to both u an...
 11.4.14: In Exercises 1116, find and show that it is orthogonal to both u an...
 11.4.15: In Exercises 1116, find and show that it is orthogonal to both u an...
 11.4.16: In Exercises 1116, find and show that it is orthogonal to both u an...
 11.4.17: Think About It In Exercises 1720, use the vectors u and v shown in ...
 11.4.18: Think About It In Exercises 1720, use the vectors u and v shown in ...
 11.4.19: Think About It In Exercises 1720, use the vectors u and v shown in ...
 11.4.20: Think About It In Exercises 1720, use the vectors u and v shown in ...
 11.4.21: In Exercises 2124, use a computer algebra system to find and a unit...
 11.4.22: In Exercises 2124, use a computer algebra system to find and a unit...
 11.4.23: In Exercises 2124, use a computer algebra system to find and a unit...
 11.4.24: In Exercises 2124, use a computer algebra system to find and a unit...
 11.4.25: Programming Given the vectors and in component form, write a progra...
 11.4.26: Programming Use the program you wrote in Exercise 25 to find and fo...
 11.4.27: Area In Exercises 2730, find the area of the parallelogram that has...
 11.4.28: Area In Exercises 2730, find the area of the parallelogram that has...
 11.4.29: Area In Exercises 2730, find the area of the parallelogram that has...
 11.4.30: Area In Exercises 2730, find the area of the parallelogram that has...
 11.4.31: Area In Exercises 31 and 32, verify that the points are the vertice...
 11.4.32: Area In Exercises 31 and 32, verify that the points are the vertice...
 11.4.33: Area In Exercises 3336, find the area of the triangle with the give...
 11.4.34: Area In Exercises 3336, find the area of the triangle with the give...
 11.4.35: Area In Exercises 3336, find the area of the triangle with the give...
 11.4.36: Area In Exercises 3336, find the area of the triangle with the give...
 11.4.37: Torque A child applies the brakes on a bicycle by applying a downwa...
 11.4.38: Torque Both the magnitude and the direction of the force on a crank...
 11.4.39: Optimization A force of 60 pounds acts on the pipe wrench shown in ...
 11.4.40: Optimization A force of 200 pounds acts on the bracket shown in the...
 11.4.41: In Exercises 4144, find
 11.4.42: In Exercises 4144, find
 11.4.43: In Exercises 4144, find
 11.4.44: In Exercises 4144, find
 11.4.45: Volume In Exercises 45 and 46, use the triple scalar product to fin...
 11.4.46: Volume In Exercises 45 and 46, use the triple scalar product to fin...
 11.4.47: Volume In Exercises 47 and 48, find the volume of the parallelepipe...
 11.4.48: Volume In Exercises 47 and 48, find the volume of the parallelepipe...
 11.4.49: Define the cross product of vectors and
 11.4.50: State the geometric properties of the cross product.
 11.4.51: If the magnitudes of two vectors are doubled, how will the magnitud...
 11.4.52: The vertices of a triangle in space are and Explain how to find a v...
 11.4.53: True or False? In Exercises 5355, determine whether the statement i...
 11.4.54: True or False? In Exercises 5355, determine whether the statement i...
 11.4.55: True or False? In Exercises 5355, determine whether the statement i...
 11.4.56: Prove Theorem 11.9.
 11.4.57: In Exercises 5762, prove the property of the cross product.
 11.4.58: In Exercises 5762, prove the property of the cross product.
 11.4.59: In Exercises 5762, prove the property of the cross product.
 11.4.60: In Exercises 5762, prove the property of the cross product.
 11.4.61: In Exercises 5762, prove the property of the cross product.
 11.4.62: In Exercises 5762, prove the property of the cross product.
 11.4.63: Prove if and are orthogonal.
 11.4.64: Prove
Solutions for Chapter 11.4: The Cross Product of Two Vectors in Space
Full solutions for Calculus  8th Edition
ISBN: 9780618502981
Solutions for Chapter 11.4: The Cross Product of Two Vectors in Space
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Chapter 11.4: The Cross Product of Two Vectors in Space includes 64 full stepbystep solutions. This textbook survival guide was created for the textbook: Calculus, edition: 8. Calculus was written by and is associated to the ISBN: 9780618502981. Since 64 problems in chapter 11.4: The Cross Product of Two Vectors in Space have been answered, more than 76568 students have viewed full stepbystep solutions from this chapter.

Ambiguous case
The case in which two sides and a nonincluded angle can determine two different triangles

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

Component form of a vector
If a vector’s representative in standard position has a terminal point (a,b) (or (a, b, c)) , then (a,b) (or (a, b, c)) is the component form of the vector, and a and b are the horizontal and vertical components of the vector (or a, b, and c are the x, y, and zcomponents of the vector, respectively)

Conditional probability
The probability of an event A given that an event B has already occurred

Correlation coefficient
A measure of the strength of the linear relationship between two variables, pp. 146, 162.

Degree of a polynomial (function)
The largest exponent on the variable in any of the terms of the polynomial (function)

Difference of complex numbers
(a + bi)  (c + di) = (a  c) + (b  d)i

Direction angle of a vector
The angle that the vector makes with the positive xaxis

Dot product
The number found when the corresponding components of two vectors are multiplied and then summed

Graph of a polar equation
The set of all points in the polar coordinate system corresponding to the ordered pairs (r,?) that are solutions of the polar equation.

Hypotenuse
Side opposite the right angle in a right triangle.

Initial side of an angle
See Angle.

Instantaneous rate of change
See Derivative at x = a.

Inverse cotangent function
The function y = cot1 x

LRAM
A Riemann sum approximation of the area under a curve ƒ(x) from x = a to x = b using x1 as the lefthand endpoint of each subinterval

Order of magnitude (of n)
log n.

Polar form of a complex number
See Trigonometric form of a complex number.

Probability simulation
A numerical simulation of a probability experiment in which assigned numbers appear with the same probabilities as the outcomes of the experiment.

Resolving a vector
Finding the horizontal and vertical components of a vector.

Standard unit vectors
In the plane i = <1, 0> and j = <0,1>; in space i = <1,0,0>, j = <0,1,0> k = <0,0,1>