Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
2 Dot Product 15 18. Use the Cauchy-Schwarz inequality to solve the following max/min problem: If the (long) diagonal of a rectangular box has length c, what is the greatest the sum of the length, width, and height of the box can be? For what shape box does the maximum occur? 19. Give an alternative proof of the Cauchy-Schwarz inequality, as follows. Let a = |x||, b = ||y||, and deduce from ||bx - ay l|20 that x y ab. Now how do you show that |x yl ab? When does equality hold? 20. (a) Letx and y be vectors with ||x || = lly|l. Prove that the vector x + y bisects the angle between x and y ||x || and b = ||y||. Prove that (b) More generally, if x and y are arbitrary nonzero vectors, let a the vector bx + ay bisects the angle between x and y. 21. Use vector methods to prove that the diagonals of a parallelogram bisect the vertex angles if and only if the parallelogram is a rhombus. 22. Given AABC with D on BC as shown in Figure 2.6. Prove that if AD bisects ZBAC, then BD|/CD| ||AB ||/|| A || . (Hint: Use Exercise 20b. Let x = AB and y = AC; give two expressions for AD in terms of x and y and use Exercise 1.1.10.)

2 Dot Product 15 18. Use the Cauchy-Schwarz inequality to solve the following max/min problem: If the (long) diagonal of a rectangular box has length c, what is the greatest the sum of the length, width, and height of the box can be? For what shape box does the maximum occur? 19. Give an alternative proof of the Cauchy-Schwarz inequality, as follows. Let a = |x||, b = ||y||, and deduce from ||bx - ay l|20 that x y ab. Now how do you show that |x yl ab? When does equality hold? 20. (a) Letx and y be vectors with ||x || = lly|l. Prove that the vector x + y bisects the angle between x and y ||x || and b = ||y||. Prove that (b) More generally, if x and y are arbitrary nonzero vectors, let a the vector bx + ay bisects the angle between x and y. 21. Use vector methods to prove that the diagonals of a parallelogram bisect the vertex angles if and only if the parallelogram is a rhombus. 22. Given AABC with D on BC as shown in Figure 2.6. Prove that if AD bisects ZBAC, then BD|/CD| ||AB ||/|| A || . (Hint: Use Exercise 20b. Let x = AB and y = AC; give two expressions for AD in terms of x and y and use Exercise 1.1.10.)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section: Chapter Questions
Problem 63RE
See similar textbooks
icon
Related questions
Topic Video
Question

Please help me solve problem 20. Thanks!

2 Dot Product 15 18. Use the Cauchy-Schwarz inequality to solve the following max/min problem: If the (long) diagonal of a rectangular box has length c, what is the greatest the sum of the length, width, and height of the box can be? For what shape box does the maximum occur? 19. Give an alternative proof of the Cauchy-Schwarz inequality, as follows. Let a = |x||, b = ||y||, and deduce from ||bx - ay l|20 that x y ab. Now how do you show that |x yl ab? When does equality hold? 20. (a) Letx and y be vectors with ||x || = lly|l. Prove that the vector x + y bisects the angle between x and y ||x || and b = ||y||. Prove that (b) More generally, if x and y are arbitrary nonzero vectors, let a the vector bx + ay bisects the angle between x and y. 21. Use vector methods to prove that the diagonals of a parallelogram bisect the vertex angles if and only if the parallelogram is a rhombus. 22. Given AABC with D on BC as shown in Figure 2.6. Prove that if AD bisects ZBAC, then BD|/CD| ||AB ||/|| A || . (Hint: Use Exercise 20b. Let x = AB and y = AC; give two expressions for AD in terms of x and y and use Exercise 1.1.10.)
Transcribed Image Text:2 Dot Product 15 18. Use the Cauchy-Schwarz inequality to solve the following max/min problem: If the (long) diagonal of a rectangular box has length c, what is the greatest the sum of the length, width, and height of the box can be? For what shape box does the maximum occur? 19. Give an alternative proof of the Cauchy-Schwarz inequality, as follows. Let a = |x||, b = ||y||, and deduce from ||bx - ay l|20 that x y ab. Now how do you show that |x yl ab? When does equality hold? 20. (a) Letx and y be vectors with ||x || = lly|l. Prove that the vector x + y bisects the angle between x and y ||x || and b = ||y||. Prove that (b) More generally, if x and y are arbitrary nonzero vectors, let a the vector bx + ay bisects the angle between x and y. 21. Use vector methods to prove that the diagonals of a parallelogram bisect the vertex angles if and only if the parallelogram is a rhombus. 22. Given AABC with D on BC as shown in Figure 2.6. Prove that if AD bisects ZBAC, then BD|/CD| ||AB ||/|| A || . (Hint: Use Exercise 20b. Let x = AB and y = AC; give two expressions for AD in terms of x and y and use Exercise 1.1.10.)
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 5 steps with 4 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Research Design Formulation
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS