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Use index notation to derive the following vector identities: (a) a (bx c) = b. (cxa) = c (ax b); . . (b) ax (bx c) = b(a c) - c(a - b); (c) ▼. (a) = (Vo) a + (V.a); V. . (d) V(a b) = (b. V)a+(a. V)b+bx (Vxa)+ ax (V x b).

Use index notation to derive the following vector identities: (a) a (bx c) = b. (cxa) = c (ax b); . . (b) ax (bx c) = b(a c) - c(a - b); (c) ▼. (a) = (Vo) a + (V.a); V. . (d) V(a b) = (b. V)a+(a. V)b+bx (Vxa)+ ax (V x 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
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Use index notation to derive the following vector identities: (a) a (bx c) = b. (cxa)= c.(a × b); . (b) ax (bx c) = b(ac) - c(a - b); (c) ▼. (a) = (VO) · a + (▼ · a); (d) ▼(a.b) = (b. V)a + (a · V)b+bx (V×a)+ ax (V x b).
Transcribed Image Text:Use index notation to derive the following vector identities: (a) a (bx c) = b. (cxa)= c.(a × b); . (b) ax (bx c) = b(ac) - c(a - b); (c) ▼. (a) = (VO) · a + (▼ · a); (d) ▼(a.b) = (b. V)a + (a · V)b+bx (V×a)+ ax (V x b).
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