Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
79. Show that if a, b are nonzero vectors such that a 1 b, then there exists a vector X such that a x X = b 15 Hint: Show that if X is orthogonal to b and is not a multiple of a, then a x X is a multiple of b.

79. Show that if a, b are nonzero vectors such that a 1 b, then there exists a vector X such that a x X = b 15 Hint: Show that if X is orthogonal to b and is not a multiple of a, then a x X is a multiple of b.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question
79
77. Let a, b, c be nonzero vectors. Assume that b and C are not parallel, and set V3ах (b х с), w = (a· c) b – (a · b) c a. Prove that: i. V lies in the plane spanned by b and C. ii. V is orthogonal to a. b. Prove that W also satisfies (i) and (ii). Conclude that V and W are parallel. c. Show algebraically that V = W (Figure 23). bxc ax (b× c) Rogawski et al., Multivariable Calculus, 4e, © 2019 W. H. Freeman and Company FIGURE 23 78. Use Exercise 77 to prove the identity (а х b) хс — ах (bxc) — (а b)с — (b:с) а 79. Show that if a, b are nonzero vectors such that a 1 D, then there exists a vector X such that a x X = b 15 Hint: Show that if X is orthogonal to b and is not a multiple of a, then a × X is a multiple of b.
Transcribed Image Text:77. Let a, b, c be nonzero vectors. Assume that b and C are not parallel, and set V3ах (b х с), w = (a· c) b – (a · b) c a. Prove that: i. V lies in the plane spanned by b and C. ii. V is orthogonal to a. b. Prove that W also satisfies (i) and (ii). Conclude that V and W are parallel. c. Show algebraically that V = W (Figure 23). bxc ax (b× c) Rogawski et al., Multivariable Calculus, 4e, © 2019 W. H. Freeman and Company FIGURE 23 78. Use Exercise 77 to prove the identity (а х b) хс — ах (bxc) — (а b)с — (b:с) а 79. Show that if a, b are nonzero vectors such that a 1 D, then there exists a vector X such that a x X = b 15 Hint: Show that if X is orthogonal to b and is not a multiple of a, then a × X is a multiple of b.
Expert Solution
steps

Step by step

Solved in 3 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS