Using index notation, prove the following identities among vectors A, B, C, and D: (a) (A x B). (B × C) × (C x A) = (A · (B × C))². (b) (A x B) x (C x D) = [A · (C x D)]B – [B - (C x D]A.
Using index notation, prove the following identities among vectors A, B, C, and D: (a) (A x B). (B × C) × (C x A) = (A · (B × C))². (b) (A x B) x (C x D) = [A · (C x D)]B – [B - (C x D]A.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![2.18 Using index notation, prove the following identities among vectors A, B, C, and D:
(a) (A x B). (B × C) × (C × A) = (A. (B x C))².
(b) (A x B) x (C x D) = [A · (C x D)]B – [B · (C x D]A.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F780f9839-f737-4aba-91a2-6210989911b1%2Fa3b60b7e-eb55-49e3-abf3-1fa00bc017c6%2Fbg8f71_processed.png&w=3840&q=75)
Transcribed Image Text:2.18 Using index notation, prove the following identities among vectors A, B, C, and D:
(a) (A x B). (B × C) × (C × A) = (A. (B x C))².
(b) (A x B) x (C x D) = [A · (C x D)]B – [B · (C x D]A.
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